Question

If the total surface area of a cube is $216c{m}^2$, then find its volume.

• A. $216c{m}^3$
• B. $1296c{m}^3$
• C. $125c{m}^3$
• D. $343c{m}^3$

Answer 1

The correct option is A

$216c{m}^3$

Given that total surface area of cube is $216c{m}^2$

We know that, total surface area of cube is $6\times {\text{(side)}}^2$

$\Rightarrow 6\times {\text{(side)}}^2=216$

$\Rightarrow {\text{(side)}}^2=\frac{216}{6}=36$

$\Rightarrow \text{side}=\sqrt{36}=6cm$

We know that volume of a cube is ${\text{(side)}}^3$

$\Rightarrow$ Volume $={\text{(side)}}^3=6^3=216c{m}^3$