Question

The lateral surface area of the cube is \[900c{m^2}\]. Find its volume.

Answer 1

Hint: We know that a cube is a closed three-dimensional figure having 6 square faces. Now, the lateral surface area of a cube is the area of the four sides. Lateral surface area \[ = 4{a^2}\] , where a is the side of the square. After calculating the value of 'a' we will use the formula of volume of a cube as follows:
Volume\[ = {a^3}\], where ‘a’ is the side of the square.

Complete step-by-step answer:
We have been given the lateral surface area of the cube as \[900c{m^2}\].
Let's draw a cube of side 'a' cm:

We know that a lateral surface of a cube \[ = 4{a^2}\]
\[\begin{array}{l} \Rightarrow 4{a^2} = 900\\ \Rightarrow {a^2} = \dfrac{{900}}{4}\\ \Rightarrow {a^2} = 225\end{array}\]
Taking square root, we get:
\[\begin{array}{l} \Rightarrow a = \sqrt {225} \\ \Rightarrow 15cm.\end{array}\]
Again, we know that, the volume of a cube \[{a^3}{\rm{ cubic\ units}}\].
So, we have, side\[\left( {\rm{a}} \right) = 1{\rm{5cm}}\].
Volume \[ = {\left( {15} \right)^3}\]
\[\begin{array}{l} \Rightarrow 15 \times 15 \times 15\\ \Rightarrow 3375{\rm{ cubic\ cm}}{\rm{.}}\end{array}\]
Therefore, the volume of the cube is 3375 cubic cm.

Note: Just be careful while finding the value of 'a' because by mistake sometimes we just equate \[{a^2} = 900\] and we missed the term 4 before \['{a^2}'\] in the equation and we get the incorrect answer.
Also, the suitable diagram according to the question is the first step you should do in this kind of question. So, that you can easily visualize the things and the next step you should do.