Question

The total surface area of a cube is $96{\mathrm{cm}}^2$. The volume of the cube is:

• A. $8{\mathrm{cm}}^3$
• B. $512{\mathrm{cm}}^3$
• C. $64{\mathrm{cm}}^3$
• D. $27{\mathrm{cm}}^3$

Answer 1

The correct option is C

$64{\mathrm{cm}}^3$

Finding volume of the cube is:

The volume of a cube is calculated with the help of total surface area.

The total surface area of cube is given as $96{\mathrm{cm}}^2$

Total surface area of cube $=6{\mathrm{a}}^2$

$$\begin{gathered} 6{\mathrm{a}}^2=96{\mathrm{cm}}^2 \\ {\mathrm{a}}^2=\frac{96}{6}=16 \\ \mathrm{a}=4 \end{gathered}$$

Volume of a cube $={\mathrm{a}}^3$

$=4^3$

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

Hence, option (C) is correct.