Question

QUIZ (1380)
Materi: Bangun Ruang

Tentukan volume kubus yang memiliki diagonal ruang sepanjang 4 cm!​

Answer 1

Bangun Ruang Sisi Tegak

[Kubus]

..

[tex]\begin{aligned} Volume &= \left(\frac{4}{\sqrt{3}}\right)^3 \\&= \left(\frac{4\sqrt{3}}{3}\right)^3 \\&= \frac{(4\sqrt{3})^3}{3^3} \\&= \frac{64 \times 3\sqrt{3}}{27} \\&= \frac{64 \times \cancel{\red{3}}\sqrt{3}}{\cancel{\red{27}}~{}^9} \\&= \boxed{\bold{\frac{64\sqrt{3}}{9} \: cm {}^{3} }} \end{aligned}[/tex]

• V Kubus = [tex]sisi^3[/tex]
• D Ruang Kubus = [tex]sisi\sqrt{3}[/tex]

[tex]\begin{array}{lr}\texttt{Selamat Hari Pendidikan Nasional}\end{array}[/tex]

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 02 - 05 - 2023}}[/tex]

Answer 2

Verified answer

PEMBAHASAN

Bangun Ruang

Kubus

rusuk = r

diagonal ruang = 4 cm

r√3 = 4

(r√3)³ = 4³

r³ × 3√3 = 64

r³ = 64/(3√3)

r³ = 64/9 √3 cm³

Volume kubus = r³ = 64/9 √3 cm³