Question

The surface area of a cube is $384{\text{cm}}^2$. Find its volume.

• A. $512{\text{cm}}^3$
• B. $556{\text{cm}}^3$
• C. $456{\text{cm}}^3$
• D. $364{\text{cm}}^3$

Answer 1

The correct option is A $512{\text{cm}}^3$

Given, surface area of cube = $384{\text{cm}}^2$
Surface area of a cube = $6a^2$
$\Rightarrow 6a^2=384$
$\Rightarrow a^2=\frac{384}{6}$
$\Rightarrow a=\sqrt{\frac{384}{6}}$
$\Rightarrow a=\sqrt{64}=8cm$

$\text{Volume of a cube}=a^3=8^3=512{\text{cm}}^3$