Question

Total surface area of a cube is $216$ $c{m}^2$, then it's volume is :

• A. $216$ $c{m}^3$
• B. $144$ $c{m}^3$
• C. $196$ $c{m}^3$
• D. $212$ $c{m}^3$

Answer 1

The correct option is A $216$ $c{m}^3$

Given, lateral surface area of a cube $=216$ cm${}^2$.

We know, total surface area of cube $=6($a${)}^2$.

$\therefore 6($a${)}^2=216$

$⟹($a${)}^2=\frac{216}{6}$

$⟹($a${)}^2=36$

$⟹$ a $=6$.

Also, volume of cube $=($ a${)}^3$.

$\therefore$ Volume of cube $=(6{)}^3=216$ cm${}^3$.

Therefore, option $A$ is correct.