Volume gabungan bangun ruang pada gambar tersebut adalah: V = volume ½ bola + volume kerucut (dengan panjang jari-jari yang sama) ⇔ V = ½·(4/3)·πr³ + (1/3)πr²t ⇔ V = (2/3)πr³ + (1/3)πr²t ⇔ V = (1/3)πr²(2r) + (1/3)πr²t ⇔ V = (1/3)πr²(2r + t) (r = 10 cm, t = 15 cm, π = 3,14) ⇔ V = (1/3)·(3,14)·10²·(2·10 + 15) ⇔ V = (1/3)·314·35 ⇔ V = (1/3)·314·(30 + 5) ⇔ V = 314·10 + (1/3)·314·5 ⇔ V = 3.140 + (1/3)·1570 ⇔ V = 3.140 + 523 ¹/₃ ∴ V = 3.663 ¹/₃ cm³ ≈ 3.663,33 cm³.
Volume gabungan:
[tex]\boxed{\,V=\bf3663\,\frac{1}{3}\ cm^3\approx3663{,}33 cm^3\,}[/tex]
Penjelasan dengan langkah-langkah
Bangun Ruang Sisi Lengkung
Volume gabungan bangun ruang pada gambar tersebut adalah:
V = volume ½ bola + volume kerucut
(dengan panjang jari-jari yang sama)
⇔ V = ½·(4/3)·πr³ + (1/3)πr²t
⇔ V = (2/3)πr³ + (1/3)πr²t
⇔ V = (1/3)πr²(2r) + (1/3)πr²t
⇔ V = (1/3)πr²(2r + t)
(r = 10 cm, t = 15 cm, π = 3,14)
⇔ V = (1/3)·(3,14)·10²·(2·10 + 15)
⇔ V = (1/3)·314·35
⇔ V = (1/3)·314·(30 + 5)
⇔ V = 314·10 + (1/3)·314·5
⇔ V = 3.140 + (1/3)·1570
⇔ V = 3.140 + 523 ¹/₃
∴ V = 3.663 ¹/₃ cm³ ≈ 3.663,33 cm³.