Question:
The volume of a cube is 512 cm3. Its total surface area is
(a) 256 cm2
(b) 384 cm2
(c) 512 cm2
(d) 64 cm2
Solution:
(b) $384 \mathrm{~cm}^{2}$
Suppose that a cm is the edge of the cube.
We have:
$a^{3}=512$
$\Rightarrow a=\sqrt[3]{512}=8 \mathrm{~cm}$
$\therefore$ Total surface area of cube $=6 a^{2} \mathrm{~cm}^{2}$
$=6 \times 8 \times 8 \mathrm{~cm}^{2}=384 \mathrm{~cm}^{2}$