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Wajib.","2026-10-08T09:24:41.433Z",{"id":297,"subjectId":15,"levelId":55,"parentId":98,"slug":1455,"name":1456,"description":1457,"order":1458,"createdAt":1459,"updatedAt":1459},"matriks","Matriks","Matriks — Kelas 11 Lanjut.",13,"2026-10-08T09:24:41.441Z",{"id":1461,"subjectId":24,"levelId":55,"parentId":98,"slug":1462,"name":1463,"description":1464,"order":1458,"createdAt":1465,"updatedAt":1465},"cmuzbyhhz003k71r9s7s8evk1","rangkaian-pegas","Rangkaian Pegas","Rangkaian Pegas — Kelas 11.","2026-10-08T09:24:41.111Z",{"id":159,"subjectId":24,"levelId":55,"parentId":98,"slug":1467,"name":1468,"description":1469,"order":1470,"createdAt":1471,"updatedAt":1471},"fluida","Fluida","Fluida — Kelas 11.",14,"2026-10-08T09:24:41.113Z",{"id":273,"subjectId":15,"levelId":55,"parentId":98,"slug":1473,"name":1474,"description":1475,"order":1470,"createdAt":1476,"updatedAt":1476},"polinomial","Polinomial","Polinomial — Kelas 11 Lanjut.","2026-10-08T09:24:41.454Z",{"id":189,"subjectId":15,"levelId":55,"parentId":98,"slug":1478,"name":1479,"description":1480,"order":1481,"createdAt":1482,"updatedAt":1482},"fungsi-trigonometri","Fungsi Trigonometri","Fungsi Trigonometri — Kelas 11 Lanjut.",15,"2026-10-08T09:24:41.469Z",{"id":183,"subjectId":24,"levelId":55,"parentId":98,"slug":1484,"name":1485,"description":1486,"order":1481,"createdAt":1487,"updatedAt":1487},"gerak-harmonik-sederhana-ghs","Gerak Harmonik Sederhana (GHS)","Gerak Harmonik Sederhana (GHS) — Kelas 11.","2026-10-08T09:24:41.119Z",{"id":213,"subjectId":24,"levelId":55,"parentId":98,"slug":1489,"name":1490,"description":1491,"order":1492,"createdAt":1493,"updatedAt":1493},"gelombang-mekanik","Gelombang Mekanik","Gelombang Mekanik — Kelas 11.",16,"2026-10-08T09:24:41.132Z",{"id":279,"subjectId":15,"levelId":55,"parentId":98,"slug":1248,"name":1249,"description":1495,"order":1492,"createdAt":1496,"updatedAt":1496},"Vektor — Kelas 11 Lanjut.","2026-10-08T09:24:41.485Z",{"id":135,"subjectId":24,"levelId":55,"parentId":98,"slug":1498,"name":1499,"description":1500,"order":1501,"createdAt":1502,"updatedAt":1502},"gelombang-cahaya","Gelombang Cahaya","Gelombang Cahaya — Kelas 11.",17,"2026-10-08T09:24:41.150Z",{"id":219,"subjectId":15,"levelId":55,"parentId":98,"slug":1504,"name":1505,"description":1506,"order":1501,"createdAt":1507,"updatedAt":1507},"transformasi-geometri","Transformasi Geometri","Transformasi Geometri — Kelas 11 Lanjut.","2026-10-08T09:24:41.498Z",{"id":165,"subjectId":15,"levelId":55,"parentId":98,"slug":1509,"name":1510,"description":1511,"order":1512,"createdAt":1513,"updatedAt":1513},"fungsi-dan-pemodelannya","Fungsi dan Pemodelannya","Fungsi dan Pemodelannya — Kelas 11 Lanjut.",18,"2026-10-08T09:24:41.504Z",{"id":201,"subjectId":24,"levelId":55,"parentId":98,"slug":1515,"name":1516,"description":1517,"order":1512,"createdAt":1518,"updatedAt":1518},"optik","Optik","Optik — Kelas 11.","2026-10-08T09:24:41.161Z",{"id":75,"subjectId":15,"levelId":55,"parentId":98,"slug":1520,"name":83,"description":1521,"order":1522,"createdAt":1523,"updatedAt":1523},"barisan-dan-deret-kelas-12-wajib","Barisan dan Deret — Kelas 12 Wajib.",19,"2026-10-08T09:24:41.512Z",{"id":374,"subjectId":24,"levelId":55,"parentId":98,"slug":1525,"name":1526,"description":1527,"order":1522,"createdAt":1528,"updatedAt":1528},"suhu-dan-kalor","Suhu dan Kalor","Suhu dan Kalor — Kelas 11.","2026-10-08T09:24:41.169Z",{"id":105,"subjectId":15,"levelId":55,"parentId":98,"slug":1530,"name":1531,"description":1532,"order":1533,"createdAt":1534,"updatedAt":1534},"bunga","Bunga","Bunga — Kelas 12 Wajib.",20,"2026-10-08T09:24:41.518Z",{"id":171,"subjectId":24,"levelId":55,"parentId":98,"slug":1536,"name":1537,"description":1538,"order":1533,"createdAt":1539,"updatedAt":1539},"teori-kinetik-gas","Teori Kinetik Gas","Teori Kinetik Gas — Kelas 11.","2026-10-08T09:24:41.188Z",{"id":380,"subjectId":15,"levelId":55,"parentId":98,"slug":1541,"name":1542,"description":1543,"order":1544,"createdAt":1545,"updatedAt":1545},"investasi-dan-pinjaman","Investasi dan Pinjaman","Investasi dan Pinjaman — Kelas 12 Wajib.",21,"2026-10-08T09:24:41.525Z",{"id":398,"subjectId":24,"levelId":55,"parentId":98,"slug":1547,"name":1548,"description":1549,"order":1544,"createdAt":1550,"updatedAt":1550},"termodinamika","Termodinamika","Termodinamika — Kelas 11.","2026-10-08T09:24:41.202Z",{"id":326,"subjectId":15,"levelId":55,"parentId":98,"slug":1552,"name":1553,"description":1554,"order":1555,"createdAt":1556,"updatedAt":1556},"kaidah-pencacahan","Kaidah Pencacahan","Kaidah Pencacahan — Kelas 12 Wajib.",22,"2026-10-08T09:24:41.540Z",{"id":267,"subjectId":24,"levelId":55,"parentId":98,"slug":1558,"name":1559,"description":1560,"order":1555,"createdAt":1561,"updatedAt":1561},"listrik-statis","Listrik Statis","Listrik Statis — Kelas 12.","2026-10-08T09:24:41.215Z",{"id":237,"subjectId":24,"levelId":55,"parentId":98,"slug":1563,"name":1564,"description":1565,"order":1566,"createdAt":1567,"updatedAt":1567},"listrik-arus-searah","Listrik Arus Searah","Listrik Arus Searah — Kelas 12.",23,"2026-10-08T09:24:41.227Z",{"id":285,"subjectId":15,"levelId":55,"parentId":98,"slug":1569,"name":1418,"description":1570,"order":1566,"createdAt":1571,"updatedAt":1571},"peluang-kelas-12-wajib","Peluang — Kelas 12 Wajib.","2026-10-08T09:24:41.547Z",{"id":249,"subjectId":15,"levelId":55,"parentId":98,"slug":1573,"name":1574,"description":1575,"order":1576,"createdAt":1577,"updatedAt":1577},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":243,"subjectId":24,"levelId":55,"parentId":98,"slug":1579,"name":1580,"description":1581,"order":1576,"createdAt":1582,"updatedAt":1582},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":117,"subjectId":15,"levelId":55,"parentId":98,"slug":1584,"name":1585,"description":1586,"order":1587,"createdAt":1588,"updatedAt":1588},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":68,"subjectId":24,"levelId":55,"parentId":98,"slug":1590,"name":1591,"description":1592,"order":1587,"createdAt":1593,"updatedAt":1593},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":308,"subjectId":24,"levelId":55,"parentId":98,"slug":1595,"name":1596,"description":1597,"order":1598,"createdAt":1599,"updatedAt":1599},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":123,"subjectId":15,"levelId":55,"parentId":98,"slug":1601,"name":1602,"description":1603,"order":1598,"createdAt":1604,"updatedAt":1604},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":332,"subjectId":15,"levelId":55,"parentId":98,"slug":1606,"name":1607,"description":1608,"order":1609,"createdAt":1610,"updatedAt":1610},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":362,"subjectId":24,"levelId":55,"parentId":98,"slug":1612,"name":1613,"description":1614,"order":1609,"createdAt":1615,"updatedAt":1615},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":207,"subjectId":15,"levelId":55,"parentId":98,"slug":1617,"name":1618,"description":1619,"order":1620,"createdAt":1621,"updatedAt":1621},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":350,"subjectId":24,"levelId":55,"parentId":98,"slug":1623,"name":1624,"description":1625,"order":1620,"createdAt":1626,"updatedAt":1626},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":356,"subjectId":24,"levelId":55,"parentId":98,"slug":1628,"name":1629,"description":1630,"order":1631,"createdAt":1632,"updatedAt":1632},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":255,"subjectId":15,"levelId":55,"parentId":98,"slug":1634,"name":1635,"description":1636,"order":1631,"createdAt":1637,"updatedAt":1637},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":147,"subjectId":15,"levelId":55,"parentId":98,"slug":1639,"name":1640,"description":1641,"order":1642,"createdAt":1643,"updatedAt":1643},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":291,"subjectId":24,"levelId":55,"parentId":98,"slug":1645,"name":1646,"description":1647,"order":1642,"createdAt":1648,"updatedAt":1648},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1650,"subjectId":15,"levelId":55,"parentId":98,"slug":1651,"name":1652,"description":1653,"order":1654,"createdAt":1655,"updatedAt":1655},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1657,"subjectId":15,"levelId":55,"parentId":98,"slug":1658,"name":1659,"description":1660,"order":1661,"createdAt":1662,"updatedAt":1662},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1664,"subjectId":15,"levelId":55,"parentId":98,"slug":1665,"name":1666,"description":1667,"order":1668,"createdAt":1669,"updatedAt":1669},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":1671,"subjectId":15,"levelId":60,"parentId":98,"slug":1672,"name":125,"description":1673,"order":1674,"createdAt":1675,"updatedAt":1675},"demo-v2-topic-matematika-kuliah-1","definisi-turunan-limit","Definisi turunan dengan limit f′(x) = lim [f(x+h) − f(x)]\u002Fh, langkah menghitungnya, gradien garis singgung, syarat diferensiabel, dan contoh soal.",100,"2026-10-14T16:01:44.645Z",{"id":1677,"subjectId":15,"levelId":55,"parentId":98,"slug":1678,"name":1679,"description":1680,"order":1674,"createdAt":1681,"updatedAt":1681},"demo-v2-topic-matematika-sma-1","fungsi-kuadrat","Fungsi Kuadrat","Fungsi kuadrat f(x) = ax² + bx + c: pengaruh a, b, c pada grafik, rumus titik puncak, sumbu simetri, diskriminan, dan contoh soal nilai maksimum.","2026-10-14T16:01:44.503Z",{"id":1683,"subjectId":33,"levelId":55,"parentId":98,"slug":1684,"name":1685,"description":1686,"order":1674,"createdAt":1687,"updatedAt":1687},"demo-v2-topic-pemrograman-sma-1","fungsi-python-def-return","Fungsi Python","Pelajari cara membuat fungsi Python dengan def, parameter, nilai default, dan return, plus perbedaan return dan print lewat contoh program yang jelas.","2026-10-14T16:01:45.616Z",{"id":1689,"subjectId":24,"levelId":49,"parentId":98,"slug":1690,"name":1691,"description":1692,"order":1674,"createdAt":1693,"updatedAt":1693},"demo-v2-topic-fisika-smp-1","glb-dan-glbb","GLB dan GLBB","Rumus GLB dan GLBB lengkap: jarak, kecepatan, percepatan, grafik posisi–waktu, perbedaan GLB dan GLBB, plus contoh soal gerak lurus dan pembahasannya.","2026-10-14T16:01:44.924Z",{"id":1695,"subjectId":24,"levelId":60,"parentId":98,"slug":1696,"name":1697,"description":1698,"order":1674,"createdAt":1699,"updatedAt":1699},"demo-v2-topic-fisika-kuliah-1","gerak-harmonik-sederhana","Gerak Harmonik Sederhana","Gerak harmonik sederhana untuk fisika dasar: persamaan x = A cos(ωt + φ), kecepatan, percepatan, periode pegas dan bandul, energi, serta contoh soal.","2026-10-14T16:01:45.223Z",{"id":1701,"subjectId":24,"levelId":55,"parentId":98,"slug":1702,"name":1703,"description":1704,"order":1674,"createdAt":1705,"updatedAt":1705},"demo-v2-topic-fisika-sma-1","hukum-newton-2","Hukum Newton 2","Hukum Newton 2: bunyi, rumus ΣF = m·a, diagram gaya, gaya gesek statis dan kinetis, serta contoh soal mencari percepatan dan massa beserta pembahasan.","2026-10-14T16:01:45.084Z",{"id":1707,"subjectId":33,"levelId":60,"parentId":98,"slug":1708,"name":1709,"description":1710,"order":1674,"createdAt":1711,"updatedAt":1711},"demo-v2-topic-pemrograman-kuliah-1","notasi-big-o-kompleksitas-waktu","Notasi Big O","Pahami notasi Big O dan kompleksitas waktu algoritma: O(1), O(log n), O(n), O(n²), cara menghitungnya dari kode Python, dan contoh soalnya.","2026-10-14T16:01:45.769Z",{"id":1713,"subjectId":33,"levelId":43,"parentId":98,"slug":1714,"name":1715,"description":1716,"order":1674,"createdAt":1717,"updatedAt":1717},"demo-v2-topic-pemrograman-sd-1","pengertian-algoritma","Pengertian Algoritma","Algoritma adalah langkah-langkah urut untuk menyelesaikan masalah. Pelajari pengertian, ciri, dan contoh algoritma sehari-hari untuk siswa SD.","2026-10-14T16:01:45.355Z",{"id":1719,"subjectId":24,"levelId":43,"parentId":98,"slug":1720,"name":1721,"description":1722,"order":1674,"createdAt":1723,"updatedAt":1723},"demo-v2-topic-fisika-sd-1","pengukuran-panjang","Pengukuran Panjang","Belajar pengukuran panjang untuk SD: satuan baku, alat ukur panjang, cara memakai penggaris, dan tangga satuan panjang km sampai mm + contoh soal.","2026-10-14T16:01:44.803Z",{"id":1725,"subjectId":15,"levelId":43,"parentId":98,"slug":1726,"name":1727,"description":1728,"order":1674,"createdAt":1729,"updatedAt":1729},"demo-v2-topic-matematika-sd-1","penjumlahan-pecahan","Penjumlahan Pecahan","Cara penjumlahan pecahan berpenyebut sama dan beda penyebut memakai KPK, pecahan senilai, dan pecahan campuran, lengkap dengan contoh soal SD.","2026-10-14T16:01:44.034Z",{"id":1731,"subjectId":15,"levelId":49,"parentId":98,"slug":1732,"name":1733,"description":1734,"order":1674,"createdAt":1735,"updatedAt":1735},"demo-v2-topic-matematika-smp-1","teorema-pythagoras","Teorema Pythagoras","Teorema Pythagoras a² + b² = c² untuk mencari sisi miring dan sisi siku-siku, tripel Pythagoras, diagonal ruang balok, dan contoh soal kelas 8.","2026-10-14T16:01:44.305Z",{"id":1737,"subjectId":33,"levelId":49,"parentId":98,"slug":1738,"name":1739,"description":1740,"order":1674,"createdAt":1741,"updatedAt":1741},"demo-v2-topic-pemrograman-smp-1","variabel-dan-tipe-data-python","Variabel dan Tipe Data Python","Belajar variabel dan tipe data Python dari nol: int, float, string, boolean, operator, print, dan input, lengkap dengan contoh program dan latihan.","2026-10-14T16:01:45.472Z",{"id":1743,"subjectId":33,"levelId":60,"parentId":98,"slug":1744,"name":1745,"description":1746,"order":1747,"createdAt":1748,"updatedAt":1748},"demo-v2-topic-pemrograman-kuliah-2","class-dan-object-python","Class dan Object Python","Pelajari class dan object Python untuk OOP: __init__, self, atribut, method, inheritance, dan invarian objek lewat contoh program dompet digital.",101,"2026-10-14T16:01:45.800Z",{"id":1750,"subjectId":15,"levelId":55,"parentId":98,"slug":1751,"name":1752,"description":1753,"order":1747,"createdAt":1754,"updatedAt":1754},"demo-v2-topic-matematika-sma-2","eksponen-dan-logaritma","Eksponen dan Logaritma","Materi eksponen dan logaritma kelas 10: sifat-sifat eksponen, definisi dan sifat logaritma, persamaan eksponen dan logaritma, serta contoh soal.","2026-10-14T16:01:44.555Z",{"id":1756,"subjectId":24,"levelId":43,"parentId":98,"slug":1757,"name":1758,"description":1759,"order":1747,"createdAt":1760,"updatedAt":1760},"demo-v2-topic-fisika-sd-2","macam-macam-gaya","Gaya dan Macam-Macamnya","Gaya adalah tarikan atau dorongan. Pelajari macam-macam gaya (otot, gravitasi, magnet, gesek, pegas), pengaruhnya pada benda, dan contoh soalnya.","2026-10-14T16:01:44.840Z",{"id":1762,"subjectId":15,"levelId":43,"parentId":98,"slug":1763,"name":1764,"description":1765,"order":1747,"createdAt":1766,"updatedAt":1766},"demo-v2-topic-matematika-sd-2","rumus-keliling-dan-luas-bangun-datar","Keliling dan Luas Bangun Datar","Rumus keliling dan luas bangun datar: persegi, persegi panjang, segitiga, jajargenjang, trapesium, dan lingkaran, dengan cara mudah dan contoh soal.","2026-10-14T16:01:44.140Z",{"id":1768,"subjectId":33,"levelId":55,"parentId":98,"slug":1769,"name":1770,"description":1771,"order":1747,"createdAt":1772,"updatedAt":1772},"demo-v2-topic-pemrograman-sma-2","list-dan-dictionary-python","List dan Dictionary Python","Pahami list dan dictionary Python: indeks, append, key-value, get, dan perulangan, plus perbedaan keduanya lewat contoh pengolahan data nilai siswa.","2026-10-14T16:01:45.659Z",{"id":1774,"subjectId":24,"levelId":49,"parentId":98,"slug":1775,"name":1776,"description":1777,"order":1747,"createdAt":1778,"updatedAt":1778},"demo-v2-topic-fisika-smp-2","rumus-massa-jenis","Massa Jenis","Rumus massa jenis ρ = m\u002FV lengkap dengan satuan kg\u002Fm³ dan g\u002Fcm³, tabel massa jenis air, besi, dan minyak, cara menghitung, serta contoh soal pembahasan.","2026-10-14T16:01:44.967Z",{"id":1780,"subjectId":33,"levelId":49,"parentId":98,"slug":1781,"name":1782,"description":1783,"order":1747,"createdAt":1784,"updatedAt":1784},"demo-v2-topic-pemrograman-smp-2","percabangan-python-if-else","Percabangan Python","Pelajari percabangan Python dengan if, elif, dan else: operator perbandingan, operator logika, dan contoh program nilai rapor lengkap dengan outputnya.","2026-10-14T16:01:45.518Z",{"id":1786,"subjectId":33,"levelId":43,"parentId":98,"slug":1787,"name":1788,"description":1789,"order":1747,"createdAt":1790,"updatedAt":1790},"demo-v2-topic-pemrograman-sd-2","percabangan-dalam-algoritma","Percabangan dalam Algoritma","Percabangan dalam algoritma memilih tindakan berdasarkan syarat jika-maka. Pelajari pengertian, contoh sehari-hari, dan simbol flowchart-nya.","2026-10-14T16:01:45.408Z",{"id":1792,"subjectId":15,"levelId":49,"parentId":98,"slug":1793,"name":1794,"description":1795,"order":1747,"createdAt":1796,"updatedAt":1796},"demo-v2-topic-matematika-smp-2","persamaan-garis-lurus","Persamaan Garis Lurus","Persamaan garis lurus y = mx + c, rumus gradien dari dua titik, garis sejajar dan tegak lurus, cara menggambar grafik, serta contoh soal kelas 8.","2026-10-14T16:01:44.363Z",{"id":1798,"subjectId":24,"levelId":60,"parentId":98,"slug":1799,"name":1800,"description":1801,"order":1747,"createdAt":1802,"updatedAt":1802},"demo-v2-topic-fisika-kuliah-2","usaha-oleh-gaya-berubah","Usaha Gaya Berubah","Usaha oleh gaya berubah dengan integral W = ∫F dx, rumus usaha W = F·s sebagai dot product, usaha pegas, dan teorema usaha–energi, plus contoh soal.","2026-10-14T16:01:45.258Z",{"id":1804,"subjectId":15,"levelId":55,"parentId":98,"slug":1805,"name":1806,"description":1807,"order":1808,"createdAt":1809,"updatedAt":1809},"demo-v2-topic-matematika-sma-3","rumus-peluang","Peluang Kejadian","Rumus peluang P(A) = n(A)\u002Fn(S), ruang sampel, peluang komplemen, frekuensi harapan, kejadian saling lepas dan saling bebas, plus contoh soal dadu dan koin.",102,"2026-10-14T16:01:44.588Z",{"id":1811,"subjectId":33,"levelId":55,"parentId":98,"slug":1812,"name":1813,"description":1814,"order":1808,"createdAt":1815,"updatedAt":1815},"demo-v2-topic-pemrograman-sma-3","pencarian-linear-dan-biner","Pencarian Linear dan Biner","Pelajari pencarian linear dan pencarian biner (binary search): cara kerja, syarat data terurut, kode Python, dan perbandingan jumlah langkahnya.","2026-10-14T16:01:45.700Z",{"id":1817,"subjectId":33,"levelId":49,"parentId":98,"slug":1818,"name":1819,"description":1820,"order":1808,"createdAt":1821,"updatedAt":1821},"demo-v2-topic-pemrograman-smp-3","perulangan-python-for-while","Perulangan Python","Pelajari perulangan Python dengan for, range(), dan while, lengkap dengan contoh program menghitung total, break, continue, dan latihan soal.","2026-10-14T16:01:45.560Z",{"id":1823,"subjectId":33,"levelId":43,"parentId":98,"slug":1824,"name":1825,"description":1826,"order":1808,"createdAt":1827,"updatedAt":1827},"demo-v2-topic-pemrograman-sd-3","perulangan-dalam-algoritma","Perulangan dalam Algoritma","Perulangan dalam algoritma mengulang langkah yang sama beberapa kali. Pelajari pengertian, contoh perulangan sehari-hari, dan cara menghitung hasilnya.","2026-10-14T16:01:45.436Z",{"id":1829,"subjectId":15,"levelId":49,"parentId":98,"slug":1830,"name":1831,"description":1832,"order":1808,"createdAt":1833,"updatedAt":1833},"demo-v2-topic-matematika-smp-3","rumus-prisma-dan-limas","Prisma dan Limas","Rumus volume prisma dan limas, luas permukaan, sifat sisi-rusuk-titik sudut, jaring-jaring, limas 3D interaktif, dan contoh soal bangun ruang sisi datar.","2026-10-14T16:01:44.400Z",{"id":1835,"subjectId":33,"levelId":60,"parentId":98,"slug":1836,"name":1837,"description":1838,"order":1808,"createdAt":1839,"updatedAt":1839},"demo-v2-topic-pemrograman-kuliah-3","unit-test-python","Unit Test Python","Pelajari unit test Python dengan modul unittest: assertEqual, assertRaises, nilai batas, dan cara menjalankan tes, lengkap dengan contoh dan versi pytest.","2026-10-14T16:01:45.832Z",{"id":1841,"subjectId":15,"levelId":60,"parentId":98,"slug":1842,"name":1843,"description":1844,"order":1808,"createdAt":1845,"updatedAt":1845},"demo-v2-topic-matematika-kuliah-3","vektor-3-dimensi-dot-product","Vektor 3D dan Dot Product","Vektor 3 dimensi: komponen, panjang vektor, vektor satuan, dot product atau perkalian titik, sudut antara dua vektor, proyeksi, dan contoh soal.","2026-10-14T16:01:44.715Z",{"id":1847,"subjectId":15,"levelId":43,"parentId":98,"slug":1848,"name":1849,"description":1850,"order":1808,"createdAt":1851,"updatedAt":1851},"demo-v2-topic-matematika-sd-3","rumus-volume-kubus","Volume dan Luas Permukaan Kubus","Rumus volume kubus V = s³ dan luas permukaan kubus L = 6s², sifat kubus, jaring-jaring, kubus 3D interaktif, dan contoh soal bertingkat.","2026-10-14T16:01:44.189Z",{"id":1853,"subjectId":15,"levelId":49,"parentId":98,"slug":1854,"name":1855,"description":1856,"order":1857,"createdAt":1858,"updatedAt":1858},"demo-v2-topic-matematika-smp-4","rumus-tabung-dan-kerucut","Tabung dan Kerucut","Rumus volume tabung dan kerucut, luas permukaan, garis pelukis, jaring-jaring berupa persegi panjang dan juring, kerucut 3D interaktif, dan contoh soal.",103,"2026-10-14T16:01:44.438Z",{"id":1860,"subjectId":33,"levelId":55,"parentId":98,"slug":1861,"name":1862,"description":1863,"order":1857,"createdAt":1864,"updatedAt":1864},"demo-v2-topic-pemrograman-sma-4","try-except-python","Try Except dan Membaca File","Pelajari try except Python untuk menangani error seperti ValueError dan FileNotFoundError, serta cara membaca dan menulis file txt dengan with open.","2026-10-14T16:01:45.731Z",{"id":1866,"subjectId":15,"levelId":43,"parentId":98,"slug":1867,"name":1868,"description":1869,"order":1857,"createdAt":1870,"updatedAt":1870},"demo-v2-topic-matematika-sd-4","rumus-volume-balok","Volume dan Luas Permukaan Balok","Rumus volume balok V = p × l × t dan luas permukaan balok L = 2(pl + pt + lt), sifat balok, jaring-jaring, balok 3D interaktif, dan contoh soal.","2026-10-14T16:01:44.239Z",[1872,1875,1880,1885],{"id":1873,"slug":25,"name":26,"createdAt":1874},"cmvogd3r1000607tdh34zf0vv","2026-10-25T23:22:15.997Z",{"id":1876,"slug":1877,"name":1878,"createdAt":1879},"cmvogctp7000507tdmugcad1g","fisika-statistik","Fisika Statistik","2026-10-25T23:22:02.971Z",{"id":1881,"slug":1882,"name":1883,"createdAt":1884},"cmvhrhrvm00027m1risodrm04","onmipa","ONMIPA","2026-10-21T06:59:26.435Z",{"id":1886,"slug":1887,"name":1887,"createdAt":1888},"cmvhrhm2s00017m1rpjm53zrv","tag","2026-10-21T06:59:18.917Z",{"id":1890,"type":1891,"slug":1892,"title":1893,"excerpt":1894,"coverUrl":98,"status":1895,"publishedAt":1896,"featured":4,"subjectId":15,"blocks":1897,"seoTitle":98,"seoDescription":98,"readingMinutes":1414,"order":21,"hiddenFromOthers":4,"createdAt":1993,"updatedAt":1993,"subject":1994,"levels":1995,"topics":1998,"tags":1999,"lang":2000,"alternates":2001,"author":98,"resolved":2003,"related":2015,"sequence":98},"demo-v2-a-rumus-bangun-ruang","ARTICLE","rumus-bangun-ruang","Rumus Bangun Ruang Lengkap: Volume dan Luas Permukaan + Contoh","Rumus bangun ruang lengkap: volume dan luas permukaan kubus, balok, prisma, limas, tabung, kerucut, dan bola dalam satu tabel, plus konversi liter.","PUBLISHED","2026-10-14T16:01:44.770Z",[1898,1903,1910,1914,1918,1922,1926,1931,1938,1942,1946,1951,1955,1959,1963,1967,1973,1977,1981,1985,1989],{"id":1899,"data":1900,"type":1902},"s1-1",{"markdown":1901},"**Rumus bangun ruang** terdiri atas dua jenis: rumus **volume** untuk isi ruang (satuan kubik, misalnya cm³) dan rumus **luas permukaan** untuk luas seluruh sisi (satuan persegi, misalnya cm²). Untuk kubus, balok, prisma, dan tabung, volume = luas alas × tinggi. Untuk limas dan kerucut, volume = $\\frac13$ × luas alas × tinggi. Untuk bola, $V=\\frac43\\pi r^3$. Luas permukaan selalu sama dengan jumlah luas semua sisi, yaitu luas jaring-jaringnya.","text",{"id":1904,"data":1905,"type":1909},"s1-2",{"title":1906,"variant":1907,"markdown":1908},"Tiga pola rumus volume bangun ruang","info","Bangun tegak (kubus, balok, prisma, tabung): $V=L_{\\text{alas}}\\times t$\n\nBangun runcing (limas, kerucut): $V=\\frac13\\times L_{\\text{alas}}\\times t$\n\nBola: $V=\\frac43\\pi r^3$","callout",{"id":1911,"data":1912,"type":1902},"s2-1",{"markdown":1913},"## Tabel Rumus Volume dan Luas Permukaan Bangun Ruang\n\n| Bangun ruang | Rumus volume | Rumus luas permukaan |\n|---|---|---|\n| Kubus (rusuk $s$) | $s^3$ | $6s^2$ |\n| Balok | $p\\times l\\times t$ | $2(pl+pt+lt)$ |\n| Prisma | $L_{\\text{alas}}\\times t$ | $2L_{\\text{alas}}+K_{\\text{alas}}\\times t$ |\n| Limas | $\\frac13\\times L_{\\text{alas}}\\times t$ | $L_{\\text{alas}}+$ jumlah luas sisi tegak |\n| Tabung | $\\pi r^2t$ | $2\\pi r(r+t)$ |\n| Kerucut | $\\frac13\\pi r^2t$ | $\\pi r(r+s)$ |\n| Bola | $\\frac43\\pi r^3$ | $4\\pi r^2$ |\n\nKeterangan: $p$, $l$, $t$ adalah panjang, lebar, dan tinggi; $r$ jari-jari; $K_{\\text{alas}}$ keliling alas. Pada kerucut, $s$ adalah **garis pelukis**, $s=\\sqrt{r^2+t^2}$. Gunakan $\\pi\\approx\\frac{22}7$ jika jari-jari kelipatan 7, atau $\\pi\\approx3{,}14$.",{"id":1915,"data":1916,"type":1902},"s3-1",{"markdown":1917},"## Bangun Ruang Sisi Datar dan Sisi Lengkung\n\nBangun ruang dikelompokkan menurut bentuk sisinya:\n\n- **Bangun ruang sisi datar**: semua sisinya bidang datar berbentuk segi banyak. Contohnya kubus, balok, prisma, dan limas. Bangun ini memenuhi rumus Euler $S+T-R=2$.\n- **Bangun ruang sisi lengkung**: mempunyai paling sedikit satu sisi lengkung. Contohnya tabung, kerucut, dan bola. Rumusnya selalu memuat $\\pi$ karena alas atau penampangnya berbentuk lingkaran.\n\n| Bangun | Sisi | Rusuk | Titik sudut |\n|---|---|---|---|\n| Kubus dan balok | 6 | 12 | 8 |\n| Prisma segitiga | 5 | 9 | 6 |\n| Limas segi empat | 5 | 8 | 5 |\n| Tabung | 3 (2 datar, 1 lengkung) | 2 (lengkung) | 0 |\n| Kerucut | 2 (1 datar, 1 lengkung) | 1 (lengkung) | 1 (titik puncak) |\n| Bola | 1 (lengkung) | 0 | 0 |\n\nDi SD, kamu biasanya mulai dari kubus dan balok. Di SMP, daftar ini diperluas ke prisma, limas, tabung, kerucut, dan bola.",{"id":1919,"data":1920,"type":1902},"s4-1",{"markdown":1921},"## Rumus Kubus, Balok, Prisma, dan Limas\n\n### Kubus dan balok\n\n**Kubus** dibatasi 6 persegi kongruen, sehingga $V=s^3$ dan $L=6s^2$. **Balok** dibatasi 3 pasang persegi panjang, sehingga $V=p\\times l\\times t$ dan $L=2(pl+pt+lt)$. Asal-usul rumus dan latihannya dibahas di [rumus volume kubus](\u002Fmateri\u002Frumus-volume-kubus) dan [rumus volume balok](\u002Fmateri\u002Frumus-volume-balok).\n\n### Prisma dan limas\n\n**Prisma** mempunyai alas dan tutup yang kongruen serta sisi tegak berbentuk persegi panjang, jadi $V=L_{\\text{alas}}\\times t$. Semua sisi tegaknya bersama-sama membentuk satu persegi panjang selebar keliling alas, sehingga $L=2L_{\\text{alas}}+K_{\\text{alas}}\\times t$.\n\n**Limas** meruncing ke satu titik puncak. Volumenya sepertiga volume prisma yang alas dan tingginya sama: $V=\\frac13\\times L_{\\text{alas}}\\times t$. Luas permukaannya adalah luas alas ditambah semua segitiga sisi tegak. Bedakan **tinggi limas** (untuk volume) dengan **tinggi segitiga sisi tegak** (untuk luas). Pembahasan lengkapnya ada di [rumus prisma dan limas](\u002Fmateri\u002Frumus-prisma-dan-limas).",{"id":1923,"data":1924,"type":1902},"s5-1",{"markdown":1925},"## Rumus Tabung dan Kerucut\n\n### Rumus luas permukaan tabung\n\nTabung terdiri atas 2 lingkaran (alas dan tutup) dan 1 selimut. Jika selimut digunting tegak lurus alas lalu dibuka, hasilnya persegi panjang dengan panjang $2\\pi r$ (keliling alas) dan lebar $t$. Jadi:\n\n$$L_{\\text{tabung}}=2\\pi r^2+2\\pi rt=2\\pi r(r+t)$$\n\nVolume tabung tetap luas alas × tinggi: $V=\\pi r^2t$. Untuk wadah tanpa tutup, seperti gelas atau ember, kurangi satu lingkaran: $L=\\pi r^2+2\\pi rt$.\n\n### Rumus kerucut\n\nKerucut terdiri atas 1 lingkaran alas dan 1 selimut yang jika dibuka berbentuk juring lingkaran. Tiga rumus kerucut yang perlu diingat:\n\n- garis pelukis: $s=\\sqrt{r^2+t^2}$;\n- volume: $V=\\frac13\\pi r^2t$;\n- luas permukaan: $L=\\pi r^2+\\pi rs=\\pi r(r+s)$, dengan luas selimut $\\pi rs$.\n\nGaris pelukis dicari dengan [teorema Pythagoras](\u002Fmateri\u002Fteorema-pythagoras), karena $r$, $t$, dan $s$ membentuk segitiga siku-siku. Uraian lengkapnya ada di [rumus tabung dan kerucut](\u002Fmateri\u002Frumus-tabung-dan-kerucut).\n\nPada visual tabung di bawah, kamu bisa melihat sendiri selimut tabung terbuka menjadi persegi panjang.",{"id":1927,"data":1928,"type":1909},"visual-guide",{"title":1929,"variant":1907,"markdown":1930},"Eksplorasi visual","- Tekan **Jaring-jaring**, lalu geser **Buka jaring** pelan-pelan. Selimut tabung terbuka menjadi persegi panjang yang diapit dua lingkaran.\n- Geser **Jari-jari** dan perhatikan panjang persegi panjang ikut berubah, karena panjangnya sama dengan keliling alas $2\\pi r$.\n- Ubah **Tinggi**, lalu cocokkan volume dan luas permukaan di panel info dengan $\\pi r^2t$ dan $2\\pi r(r+t)$.",{"id":1932,"data":1933,"type":1937},"visual",{"height":1934,"assetId":1935,"caption":1936},520,"demo-v2-asset-cylinder","Tabung 3D interaktif dan jaring-jaringnya","interactive",{"id":1939,"data":1940,"type":1902},"s6-1",{"markdown":1941},"## Eksplorasi Visual: Selimut Tabung Menjadi Persegi Panjang\n\nUkuran awal visual adalah $r=2$ dan $t=4$. Keliling alasnya $2\\pi\\times2=4\\pi\\approx12{,}57$, jadi selimutnya persegi panjang $4\\pi\\times4$ dengan luas $16\\pi\\approx50{,}27$ satuan². Dua lingkaran menambah $2\\times\\pi\\times2^2=8\\pi$, sehingga luas permukaannya $24\\pi\\approx75{,}40$ satuan². Volumenya $\\pi\\times2^2\\times4=16\\pi\\approx50{,}27$ satuan³.\n\nAngka volume dan luas selimut di sini kebetulan sama karena $r=2$, tetapi satuannya berbeda: yang satu kubik, yang lain persegi. Ubah jari-jarinya dan kedua angka itu langsung berbeda. Visual serupa untuk kerucut ada di [kerucut 3D interaktif](\u002Finteraktif\u002Fkerucut-3d-interaktif), dan bangun ruang lainnya ada di [halaman interaktif](\u002Finteraktif).",{"id":1943,"data":1944,"type":1902},"s7-1",{"markdown":1945},"## Rumus Volume Bola dan Luas Permukaan Bola\n\n**Bola** adalah bangun ruang yang semua titik pada permukaannya berjarak sama, yaitu $r$, dari titik pusat. Bola hanya mempunyai 1 sisi lengkung dan tidak mempunyai rusuk maupun titik sudut. Contohnya bola sepak, kelereng, dan bola dunia (globe).",{"id":1947,"data":1948,"type":1909},"s7-2",{"title":1949,"variant":1907,"markdown":1950},"Rumus bola","$$V=\\frac43\\pi r^3\\qquad L=4\\pi r^2$$\nSetengah bola padat: $V=\\frac23\\pi r^3$ dan $L=2\\pi r^2+\\pi r^2=3\\pi r^2$.",{"id":1952,"data":1953,"type":1902},"s7-3",{"markdown":1954},"Dari mana rumus ini? Archimedes membandingkan bola dengan tabung yang pas membungkusnya, yaitu tabung berjari-jari $r$ dan bertinggi $2r$:\n\n- volume tabung itu $\\pi r^2\\times2r=2\\pi r^3$, dan volume bola tepat $\\frac23$ darinya: $\\frac23\\times2\\pi r^3=\\frac43\\pi r^3$;\n- luas permukaan bola sama dengan luas selimut tabung itu: $2\\pi r\\times2r=4\\pi r^2$.\n\nHubungan $V=\\frac13\\times L\\times r$ berguna untuk mengecek jawaban. Bayangkan bola tersusun dari sangat banyak limas kecil yang puncaknya di pusat bola dan tingginya $r$.\n\nPerhatikan pangkatnya: luas permukaan bola memakai $r^2$, sedangkan volume memakai $r^3$. Jika soal memberi diameter, bagi dua dulu.",{"id":1956,"data":1957,"type":1902},"s8-1",{"markdown":1958},"## Satuan Volume: cm³, Liter, dan m³\n\nKarena $1\\text{ dm}=10\\text{ cm}$, kubus bersisi 1 dm berisi $10\\times10\\times10=1.000\\text{ cm}^3$. Isi kubus inilah yang disebut **1 liter**.\n\n| Satuan | Setara dengan |\n|---|---|\n| $1\\text{ cm}^3$ | $1\\text{ mL}$ (1 cc) |\n| $1\\text{ dm}^3$ | $1\\text{ liter}=1.000\\text{ cm}^3$ |\n| $1\\text{ m}^3$ | $1.000\\text{ liter}=1.000.000\\text{ cm}^3$ |\n\nPada satuan volume, setiap turun satu tangga (m³ → dm³ → cm³) nilainya dikali 1.000, bukan 10 seperti satuan panjang atau 100 seperti satuan luas. Untuk soal liter, cara paling aman adalah mengubah semua ukuran ke dm, karena hasilnya langsung dalam liter. Hasilnya bisa kamu periksa dengan [konversi satuan volume](\u002Ftools\u002Fkalkulator\u002Fvolume).",{"id":1960,"data":1961,"type":1902},"s9-1",{"markdown":1962},"## Contoh Soal Rumus Bangun Ruang\n\n### Contoh 1: Volume dan luas permukaan bola\n\nSebuah bola berdiameter 42 cm. Hitung volume dan luas permukaannya dengan $\\pi=\\frac{22}7$.\n\n1. Jari-jari $r=42:2=21$ cm.\n2. $V=\\frac43\\times\\frac{22}7\\times21\\times21\\times21$. Sederhanakan $\\frac{22}7\\times21=66$, lalu $\\frac43\\times66=88$, sehingga $V=88\\times441=38.808\\text{ cm}^3$, sekitar 38,8 liter.\n3. $L=4\\times\\frac{22}7\\times21\\times21=4\\times66\\times21=5.544\\text{ cm}^2$.\n4. Cek dengan $V=\\frac13\\times L\\times r$: $\\frac13\\times5.544\\times21=5.544\\times7=38.808$. Cocok.\n\n### Contoh 2: Luas permukaan tabung pada kaleng\n\nKaleng tertutup berbentuk tabung mempunyai jari-jari 3,5 cm dan tinggi 10 cm. Berapa luas pelat untuk membuatnya, dan berapa isinya? Gunakan $\\pi=\\frac{22}7$.\n\n1. Luas satu lingkaran: $\\frac{22}7\\times3{,}5\\times3{,}5=38{,}5\\text{ cm}^2$.\n2. Keliling alas: $2\\times\\frac{22}7\\times3{,}5=22$ cm, jadi luas selimut $=22\\times10=220\\text{ cm}^2$.\n3. Luas permukaan $=2\\times38{,}5+220=297\\text{ cm}^2$.\n4. Volume $=38{,}5\\times10=385\\text{ cm}^3$, yaitu 385 mL.\n5. Cek dengan rumus ringkas: $2\\pi r(r+t)=22\\times13{,}5=297$. Cocok.\n\n### Contoh 3: Volume dan selimut kerucut pada tumpeng\n\nNasi tumpeng berbentuk kerucut dengan diameter alas 30 cm dan tinggi 20 cm. Dengan $\\pi=3{,}14$, berapa volumenya, dan berapa luas daun pisang untuk menutup selimutnya?\n\n1. $r=15$ cm, sehingga $s=\\sqrt{15^2+20^2}=\\sqrt{225+400}=\\sqrt{625}=25$ cm.\n2. $V=\\frac13\\times3{,}14\\times225\\times20=3{,}14\\times1.500=4.710\\text{ cm}^3$, sekitar 4,7 liter.\n3. Luas selimut $=\\pi rs=3{,}14\\times15\\times25=1.177{,}5\\text{ cm}^2$.\n4. Cek: tabung dengan alas dan tinggi yang sama bervolume $3{,}14\\times225\\times20=14.130\\text{ cm}^3$, dan sepertiganya memang 4.710 cm³.\n\n### Contoh 4: Tangki air dalam liter\n\nTangki berbentuk tabung berdiameter 1,4 m dan tinggi 2 m. Berapa liter air yang dapat ditampung? Gunakan $\\pi=\\frac{22}7$.\n\n1. Ubah ke desimeter agar hasilnya langsung liter: $r=0{,}7\\text{ m}=7\\text{ dm}$ dan $t=20\\text{ dm}$.\n2. $V=\\frac{22}7\\times7\\times7\\times20=154\\times20=3.080\\text{ dm}^3$.\n3. Karena $1\\text{ dm}^3=1\\text{ liter}$, tangki menampung 3.080 liter.\n4. Cek dalam meter kubik: $\\frac{22}7\\times0{,}7^2\\times2=3{,}08\\text{ m}^3$, dan $3{,}08\\times1.000=3.080$ liter.",{"id":1964,"data":1965,"type":1902},"s10-1",{"markdown":1966},"## Kesalahan yang Sering Terjadi",{"id":1968,"data":1969,"type":1909},"s10-2",{"title":1970,"variant":1971,"markdown":1972},"Jari-jari, bukan diameter","warning","Soal tabung, kerucut, dan bola sering memberi diameter. Memakai diameter sebagai $r$ membuat volume tabung dan kerucut menjadi 4 kali lipat, sedangkan volume bola menjadi 8 kali lipat.",{"id":1974,"data":1975,"type":1902},"s10-3",{"markdown":1976},"- Lupa faktor $\\frac13$ pada limas dan kerucut, atau sebaliknya memakai $\\frac13$ pada prisma dan tabung.\n- Memakai tinggi $t$ sebagai garis pelukis $s$ pada luas selimut kerucut.\n- Tertukar rumus bola: volume berpangkat tiga ($\\frac43\\pi r^3$), luas permukaan berpangkat dua ($4\\pi r^2$).\n- Menghitung dua lingkaran untuk wadah tanpa tutup.\n- Salah konversi: $1\\text{ liter}=1.000\\text{ cm}^3$, bukan $100\\text{ cm}^3$.",{"id":1978,"data":1979,"type":1902},"s11-1",{"markdown":1980},"## Ringkasan\n\n- Volume bangun tegak = luas alas × tinggi; bangun runcing = $\\frac13$ × luas alas × tinggi; bola $\\frac43\\pi r^3$.\n- Luas permukaan = jumlah luas semua sisi = luas jaring-jaring.\n- Tabung $L=2\\pi r(r+t)$; kerucut $L=\\pi r(r+s)$ dengan $s=\\sqrt{r^2+t^2}$; bola $L=4\\pi r^2$.\n- Sisi datar: kubus, balok, prisma, limas. Sisi lengkung: tabung, kerucut, bola.\n- $1\\text{ dm}^3=1\\text{ liter}=1.000\\text{ cm}^3$ dan $1\\text{ m}^3=1.000\\text{ liter}$.",{"id":1982,"data":1983,"type":1902},"s12-1",{"markdown":1984},"## Pertanyaan yang Sering Diajukan\n\n### Apa rumus volume bola?\n\nRumus volume bola adalah $V=\\frac43\\pi r^3$, dengan $r$ jari-jari. Bola berjari-jari 21 cm bervolume $38.808\\text{ cm}^3$ jika $\\pi=\\frac{22}7$. Jika yang diketahui diameter, bagi dua dulu untuk mendapat jari-jari.\n\n### Apa rumus luas permukaan tabung?\n\nLuas permukaan tabung tertutup adalah $2\\pi r(r+t)$, yaitu dua lingkaran $2\\pi r^2$ ditambah selimut $2\\pi rt$. Untuk tabung tanpa tutup, gunakan $\\pi r^2+2\\pi rt$. Jika hanya selimutnya, misalnya label kaleng, luasnya $2\\pi rt$.\n\n### Apa saja rumus kerucut?\n\nKerucut memakai tiga rumus: garis pelukis $s=\\sqrt{r^2+t^2}$, volume $V=\\frac13\\pi r^2t$, dan luas permukaan $L=\\pi r(r+s)$. Luas selimutnya saja adalah $\\pi rs$.\n\n### Apa beda bangun ruang sisi datar dan sisi lengkung?\n\nSemua sisi bangun ruang sisi datar (kubus, balok, prisma, limas) berupa bidang datar segi banyak. Bangun ruang sisi lengkung (tabung, kerucut, bola) mempunyai sisi lengkung, sehingga rumusnya memakai $\\pi$.\n\n### 1 liter berapa cm³?\n\nSatu liter sama dengan $1\\text{ dm}^3$ atau $1.000\\text{ cm}^3$, dan $1\\text{ m}^3=1.000$ liter. Jadi volume dalam cm³ dibagi 1.000 untuk mendapatkan liter.",{"id":1986,"data":1987,"type":1902},"s13-1",{"markdown":1988},"## Materi Terkait\n\n- [Rumus volume kubus](\u002Fmateri\u002Frumus-volume-kubus): volume $s^3$, luas permukaan $6s^2$, dan kubus 3D interaktif.\n- [Rumus volume balok](\u002Fmateri\u002Frumus-volume-balok): volume, luas permukaan, dan soal akuarium dalam liter.\n- [Rumus prisma dan limas](\u002Fmateri\u002Frumus-prisma-dan-limas): bangun ruang sisi datar dan asal faktor $\\frac13$ pada limas.\n- [Rumus tabung dan kerucut](\u002Fmateri\u002Frumus-tabung-dan-kerucut): garis pelukis, selimut, dan hubungan dengan bola.\n- [Tabung 3D interaktif](\u002Finteraktif\u002Ftabung-3d-interaktif): buka selimut tabung menjadi persegi panjang.\n- [Latihan soal tabung dan kerucut](\u002Flatihan\u002Flatihan-soal-rumus-tabung-dan-kerucut): soal pilihan ganda dengan pembahasan setiap pilihan.\n- [Jaring-jaring bangun ruang](\u002Fartikel\u002Fjaring-jaring-bangun-ruang): asal rumus luas permukaan dari jaring-jaring setiap bangun.\n- [Tryout matematika SMP](\u002Ftryout\u002Ftryout-matematika-smp): uji campuran materi SMP, termasuk prisma, limas, tabung, dan kerucut.",{"id":1990,"data":1991,"type":1902},"sources",{"markdown":1992},"## Sumber belajar\n\n- [OpenStax Prealgebra 2e — Solve Geometry Applications: Volume and Surface Area](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Fprealgebra-2e\u002Fpages\u002F9-6-solve-geometry-applications-volume-and-surface-area)\n- [OpenStax Prealgebra 2e — Geometric Formulas](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Fprealgebra-2e\u002Fpages\u002Fc-geometric-formulas)\n- [Wikipedia bahasa Indonesia — Bola (geometri)](https:\u002F\u002Fid.wikipedia.org\u002Fwiki\u002FBola_(geometri))\n- [Math is Fun — Sphere](https:\u002F\u002Fwww.mathsisfun.com\u002Fgeometry\u002Fsphere.html)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.","2026-10-14T16:01:44.772Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[1996,1997],{"id":43,"slug":44,"name":45},{"id":49,"slug":50,"name":51},[],[],"id",[2002],{"lang":2000,"slug":1892},{"assets":2004,"videos":2013,"questionSets":2014},{"demo-v2-asset-cylinder":2005},{"id":1935,"slug":2006,"kind":2007,"title":1936,"description":2008,"url":98,"posterUrl":98,"config":2009,"subject":2012},"tabung-3d-interaktif","GEOMETRY_3D","Ubah jari-jari dan tinggi tabung, lalu buka selimutnya menjadi persegi panjang selebar keliling alas.",{"shape":2010,"width":64,"height":1116,"length":1116,"radius":39,"vector":2011,"allowNet":5,"editable":5,"showAngles":5,"showLabels":5},"cylinder",[30,39,39],{"id":15,"slug":16,"name":17,"color":20},{},{},[2016,2036,2050,2063],{"id":2017,"type":1891,"slug":2018,"title":2019,"excerpt":2020,"coverUrl":98,"status":1895,"publishedAt":2021,"featured":4,"readingMinutes":1403,"order":21,"updatedAt":2022,"subject":2023,"levels":2024,"topics":2027,"tags":2030,"author":2031},"cmvxe4god001r07scxrwi3yjn","hipotesis-riemann-kuasi-bilangan-prima-ai-2026","Hipotesis Riemann dan Bilangan Prima: Terobosan AI 2026","Apa itu hipotesis Riemann dan versi kuasi yang dibuktikan AI OpenAI pada 2026? Penjelasan bilangan prima, fungsi zeta, dan pita kritis dengan contoh.","2026-11-01T05:35:03.077Z","2026-11-01T05:35:03.083Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[2025,2026],{"id":55,"slug":56,"name":57},{"id":60,"slug":61,"name":62},[2028,2029],{"id":164,"slug":166,"name":167,"subjectId":15},{"id":449,"slug":450,"name":451,"subjectId":15},[],{"name":2032,"slug":2033,"photoUrl":2034,"profession":2035},"Risyad Raflan","risyad-raflan","https:\u002F\u002Fmyfismat.com\u002Fuploads\u002F3f3eca84-9800-4c5f-97ed-1dec08f03152.jpg","Mahasiswa Jurusan Sistem Informasi",{"id":2037,"type":1891,"slug":2038,"title":2039,"excerpt":2040,"coverUrl":98,"status":1895,"publishedAt":2041,"featured":4,"readingMinutes":1414,"order":21,"updatedAt":2042,"subject":2043,"levels":2044,"topics":2047,"tags":2048,"author":2049},"cmvry76fb000c07s28zwl0iv1","matematika-pace-lari-rekor-maraton-sub-2-jam","Matematika di Balik Pace Lari dan Rekor Maraton Sub-2 Jam","Kenapa pace 6:00\u002Fkm sama dengan 10 km\u002Fjam? Bedah matematika dan fisika lari: rumus pace, prediksi Riegel, hambatan udara, dan kode Python-nya.","2026-10-28T10:09:04.009Z","2026-11-03T14:36:19.665Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[2045,2046],{"id":49,"slug":50,"name":51},{"id":55,"slug":56,"name":57},[],[],{"name":2032,"slug":2033,"photoUrl":2034,"profession":2035},{"id":2051,"type":1891,"slug":2052,"title":2053,"excerpt":2054,"coverUrl":98,"status":1895,"publishedAt":2055,"featured":4,"readingMinutes":1425,"order":21,"updatedAt":2056,"subject":2057,"levels":2058,"topics":2061,"tags":2062,"author":98},"demo-v2-a-jaring-jaring-bangun-ruang","jaring-jaring-bangun-ruang","Jaring-jaring Bangun Ruang: Kubus, Balok, Prisma, Limas, Tabung","Jaring-jaring bangun ruang: 11 jaring-jaring kubus dan cara mengeceknya, jaring balok, prisma segitiga, limas, tabung, kerucut, dan kaitannya dengan luas.","2026-10-14T16:01:44.781Z","2026-10-14T16:01:44.783Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[2059,2060],{"id":43,"slug":44,"name":45},{"id":49,"slug":50,"name":51},[],[],{"id":2064,"type":1891,"slug":2065,"title":2066,"excerpt":2067,"coverUrl":98,"status":1895,"publishedAt":2068,"featured":5,"readingMinutes":1377,"order":21,"updatedAt":2069,"subject":2070,"levels":2071,"topics":2076,"tags":2077,"author":98},"demo-v2-a-matematika","cara-belajar-matematika-dari-nol","Cara Belajar Matematika dari Nol: Urutan Materi SD–Kuliah","Cara belajar matematika dari nol: urutan materi dari pecahan, bangun ruang, aljabar, hingga kalkulus, kebiasaan belajar efektif, dan rencana 4 minggu.","2026-10-14T16:01:44.759Z","2026-10-14T16:01:44.762Z",{"id":15,"slug":16,"name":17,"color":20,"icon":19},[2072,2073,2074,2075],{"id":43,"slug":44,"name":45},{"id":49,"slug":50,"name":51},{"id":55,"slug":56,"name":57},{"id":60,"slug":61,"name":62},[],[],[2079],{"code":2000,"nativeName":2080,"isDefault":5},"Bahasa Indonesia",[]]