Question

Find the radius r of the sphere.

Answer 1

Given:

The volume of the sphere = 12348π in³

To find the radius of the sphere.

Formula

The volume of a sphere of radius r is

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

According to the problem,

`(4)/(3) \pi r^(3) = 12348\pi`

Eliminating π from both the side.

or,
`(4)/(3) r^(3)= 12348`

or,
`r^(3)=((12348)(3))/(4)`

or,
`r^(3)=9641`

or,
`r=\sqrt[3]{9261}`

or,
`r=21`

Hence,

The radius of the sphere is 21 inches.

Answer 2

21 inches

Explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

We know the volume

12348 pi = 4/3 pi r^3

Divide each side by pi

12348 pi/pi = 4/3 pi r^3 /pi

12348 = 4/3 r^3

Multiply each side by 3/4

12348 *3/4 = 4/3*3/4 r^3

9261 = r^3

Take the cubed root of each side

9261^ (1/3 ) = r^3 ^1/3

21 =r