# What is the volume of the cube if its surface area is 2400 cm^{2}?

The volume of a cube defines the number of cubic units, occupied by the cube completely.

The surface Area of a cube is the total area of all the faces of a given cube

## Answer: The volume of the cube whose area is 2400 cm^{2} is 8000 cm^{3}

To calculate the volume of the cube we will be following the below steps:

- Calculate the edge length using the surface area given
- Calculate the volume using the edge length

**Explanation:**

Surface area of a cube = 2400cm^{2} (given)

We know that,

The surface area of cube = 6a^{2}

where 'a' is the edge length of the cube

Therefore.

6a^{2} = 2400

=> a^{2} = 2400/ 6

=> a^{2} = 400

=> a = √400 (By taking square roots on both the sides)

=> a = 20 (since, √400 = 20)

Hence, a = 20cm

We know that ,

Volume of the cube = a^{3}

Therefore,

Volume of the cube = 20 × 20 × 20

=> 8000cm^{3}