Question

The total surface area of a cube is $216{\mathrm{cm}}^2$ then its volume is

• A. $216$
• B. $144$
• C. $196$
• D. $212$

Answer 1

The correct option is A

$216$

Explanation for correct option:

Option (A): The volume of a cube is calculated with the help of total surface area.

The total surface area of cube is given as $216{\mathrm{cm}}^2$.

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

$6{\mathrm{a}}^2=216{\mathrm{cm}}^2$

$$\begin{gathered} \Rightarrow {\mathrm{a}}^2=\frac{216}{6} \\ \Rightarrow {\mathrm{a}}^2=36 \\ \Rightarrow \mathrm{a}=6 \end{gathered}$$

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

$=6^3$

Volume of a cube $=216{\mathrm{cm}}^3$

Hence, option (A) is correct.

Explanation for incorrect options:

Option (B), (C), (D): Since the calculated volume of a cube is $216{\mathrm{cm}}^3$.

Hence, option (B), (C), (D) are incorrect.