Question

A where and a cylinder have the same radius and height . The volume of the cylinder is 48 cm 3. What is the volume of the sphere?

Answer 1

Given:

Sphere and cylinder have same radius and height.

Volume of the cylinder = 48 cm³

To find:

The volume of the sphere.

Solution:

Radius and height of cylinder are equal.

⇒ r = h

Volume of cylinder:

`V=\pi r^2h`

Substitute the given values.

`48=\pi r^2r` (since r = h)

`48=\pi r^3`

`48=3.14 * r^3`

Divide by 3.14 on both sides.

`$(48)/(3.14) =(3.14* r^3)/(3.14)`

`$15.28=r^3`

Taking cube root on both sides, we get

2.48 = r

The radius of the cylinder is 2.48 cm.

Sphere and cylinder have same radius and height.

Volume of sphere:

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

`$V=(4)/(3) * 3.14 * (2.48)^3`

`V=63.85`

The volume of the sphere is 63.85 cm³.