The lateral surface area of a cube is 256 m2. The volume of the cube is
Question:

The lateral surface area of a cube is 256 m2. The volume of the cube is
(a) 64 m3
(b) 216 m3
(c) 256 m3
(d) 512 m3

Solution:

(d) $512 \mathrm{~m}^{3}$

Suppose that a m be the edge of the cube.
We have:

$4 a^{2}=256$

$\Rightarrow a^{2}=\frac{256}{4}=64$

$\Rightarrow a=8 \mathrm{~m}$

$\therefore$ Volume of the cube $=a^{3} \mathrm{~m}^{3}=8^{3} \mathrm{~m}^{3}=512 \mathrm{~m}^{3}$