Question

The lateral surface area of a cube is 900 cm². Find its volume.

Answer 1

Suppose that the side of cube is x cm.
Lateral surface area of the cube = 900 cm²
$$\begin{gathered} \mathrm{Then}900=4x^2 \\ \Rightarrow x^2=\frac{900}{4}=225 \\ \Rightarrow x=\sqrt{225}=15 \end{gathered}$$
i.e., the side of the cube is 15 cm.
∴ Volume of the given cube = $x^3{\mathrm{cm}}^3={15}^3{\mathrm{cm}}^3=3375{\mathrm{cm}}^3$