Question

The total surface area of a cube is $384m^2$. Its volume will be:

• A. $343m^3$
• B. $616m^3$
• C. $512m^3$
• D. $660m^3$

Answer 1

Answer: (C)

$512m^3$

Given, lateral surface area of a cube $=384$ m${}^2$.

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

$\therefore 6($edge${)}^2=384$

$⟹($edge${)}^2=\frac{384}{6}$

$⟹($edge${)}^2=64$

$⟹$ edge $=8$.

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

$\therefore$ Volume of cube $=(8{)}^3=512$ m${}^3$.

Therefore, option $C$ is correct.