Question

Fine the volume of the sphere. Leave the answer in terms of pi.

Answer 1

Given:

The area of the given sphere = 36π in²

To find the volume of the given sphere.

We need to find the radius first.

Formula

• The area of a sphere
  `A = 4\pi r^(2)`

• The volume of the sphere
  `V = (4)/(3) \pi r^(3)`

where, r be the radius of the sphere.

Now,

According to the problem,

`4\pi r^(2) = 36\pi`

or,
`4r^(2) = 36\\` [ Eliminating π from both the side]

or,
`r^(2) = (36)/(4)`

or,
`r = √(9)`

or,
`r = 3`

So,

The radius of the sphere is 3 inches

Therefore,

The volume of the sphere is

`V = (4)/(3) \pi (3)^(3)`

or,
`V = 36\pi`

Hence,

The volume of the sphere is 36π cube inches.