Question

The lateral surface area of a cube is $100m^2$. The volume of the cube is

• A. $25m^3$
• B. $125m^3$
• C. $1000m^3$
• D. $100m^3$

Answer 1

The correct option is B

$125m^3$

Step 1: Find the edge of cube

Let$a$be the side of a cube.

Then lateral surface area of a cube$=4a^2$

Given lateral surface area of a cube is $100m^2$

$\begin{array}{rcl}4a^2& =& 100\\ a^2& =& \frac{100}{4}\\ a^2& =& 25\\ a& =& 5\end{array}$

Step 2: Find the volume of cube

$Volumeofcube=a^3=5^3=125m^3$

Hence, option b is the answer.