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Sebuah kubus memiliki diagonal ruang sebesar 12√3 cm. Tentukan volume kubus tersebut!

Rani Maharani

Soal:

Sebuah kubus memiliki diagonal ruang sebesar 12√3 cm. Tentukan volume kubus tersebut!

Jawaban:

Dalam kubus, diagonal ruang d dapat dihitung menggunakan teorema Pythagoras, yaitu d = √3s, di mana s adalah panjang sisi kubus. Maka, dengan substitusi nilai diagonal ruang yang diberikan, kita dapat menghitung besarnya s sebagai berikut:

d = √3s

12√3 cm = √3s

144 cm² = 3s²

s = √48 cm

s = 4√3 cm

Volume kubus dapat dihitung dengan rumus V = s³, yaitu:

V = (4√3 cm)³

V = 64√3 cm³

Pembahasan:

Dalam soal ini, kita diminta untuk mencari volume sebuah kubus yang memiliki diagonal ruang sebesar 12√3 cm. Pertama, kita menggunakan teorema Pythagoras untuk mencari panjang sisi kubus, dengan mengganti nilai diagonal ruang d dalam rumus d = √3s. Setelah ditemukan panjang sisi kubus, volume kubus dapat dihitung dengan rumus V = s³. Dalam hal ini, volume kubus tersebut adalah 64√3 cm³.

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