What is the volume of the cube if its surface area is 2400 cm²?

Solution:

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.

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

Surface area of the cube = 2400 cm²  (given)

We know that,

The surface area of cube = 6a²  

where 'a' is the edge length of the cube

Therefore,

6a² = 2400

⇒ a² = 2400/ 6

⇒ a² = 400

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

⇒ a = 20 (since, √400 = 20)

Hence, a = 20 cm.

We know that,

Volume of the cube = a³

Therefore,

Volume of the cube = 20 × 20 × 20

⇒ 8000 cm³

Hence, the volume of the cube whose area is 2400 cm² is 8000 cm³.

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What is the volume of the cube if its surface area is 2400 cm²?

Summary:

The volume of the cube whose area is 2400 cm² is 8000 cm³.