Question

What is the volume of the cube if it’s surface area is 2400 cm² ?

Answer 1

Hint: Here in the given question, we are provided with the surface area of the cube, and we need to find the volume of the cube. We know that a cube has all sides equal and it has six surfaces and each surface is a square, here we will find the length of the side from surface area then by using volume formulae we will get the volume of the cube.

Formulae Used: Surface area and volume of cube with side length as “a”, is given by:
\[ Area = 6{a^2}\]
\[ Volume = {a^3}\]

Complete step by step answer:
Here in the given question we first need to calculate the side length of the cube, from the surface area formula, on solving we get:
\[
   \Rightarrow Area = 6{a^2} = 2400 \\
   \Rightarrow {a^2} = \dfrac{{2400}}{6} = 400 \\
   \Rightarrow a = \sqrt {400} = 20cm \\
 \]
Here we get the length of the side of the cube, now for the volume of the cube we have:
\[ \Rightarrow Volume = {a^3} = {(20)^3} = 20 \times 20 \times 20 = 8000c{m^3}\]
Here we get the volume of the cube.

Note: In the given question we need to find the volume of the cube, here we know that volume of a cube is the product of its length, breadth and height and for cube these three values are same hence the formulae for the volume of the cube becomes side length cube.