Question

The lateral surface area of a cube is 256 m². The volume of the cube is ______.

• A. $256{\text{m}}^3$
• B. $512{\text{m}}^3$
• C. $64{\text{m}}^3$
• D. $128{\text{m}}^3$

Answer 1

The correct option is B

$512{\text{m}}^3$

Lateral surface area of cube
$=4(\text{edge}{)}^2$

$\therefore 4(\text{edge}{)}^2=256m^2$

$\Rightarrow (\text{edge}{)}^2=\frac{256}{4}$

$\Rightarrow (\text{edge}{)}^2=64$

$\Rightarrow \text{edge}=\sqrt{64}=8\text{m}$

$\text{Volume of cube}=(\text{edge}{)}^3$
$=(8{)}^3$
$=512{\text{m}}^3$