Question

A lateral surface area of the cube is $256{m^2}$. Find its volume.

Answer 1

Hint- If “a” is the side of any cube, then the volume of cube is given as ${a^3}$ In order to get the value of a we will use the simple formula of lateral surface area of cube as $4{a^2}$By using it we will get the answer.

Complete step by step answer:

Given that
Lateral surface area of cube = $256c{m^2}$
We know that the lateral surface area of cube
= $4{a^2}$
Substituting the value of area, we get
$
   \Rightarrow 4{a^2} = 256 \\
   \Rightarrow {a^2} = 64 \\
   \Rightarrow a = 8m \\
 $
We know that the volume of cube = ${a^3}$
Volume of cube = ${8^3} = 512{m^3}$
Hence, the volume of given cube is $512{m^3}$

Note- In order to solve these types of problems related to finding the area or volume and some parameters are missing such as radius for circle and side for square are not given directly in the question. Then search for the conditions given in the question to find the missing parameters. Sometimes areas are given such as in this problem. Sometimes they may give circumference.