Question

The total surface area of a cube is 96 cm². The volume of the cube is
(a) 8 cm³
(b) 27 cm³
(c) 64 cm³
(d) 512 cm³

Answer 1

(c) 64 cm³

Let a cm be the edge of the cube.
We have:
$$\begin{gathered} 6a^2=96 \\ \Rightarrow a^2=16 \\ \Rightarrow a=4\mathrm{cm} \end{gathered}$$

∴ Volume of the cube = $a^3{\mathrm{cm}}^3=4^3{\mathrm{cm}}^3=64{\mathrm{cm}}^3$