Question

A hole 2 inches in radius is drilled out of a solid sphere of radius 5 inches. Find the volume of the remaining solid.

Answer 1

The volume of remaining sphere is 489.84 cubic inches.

Explanation:

We are given the following in the question:

A hole 2 inches in radius is drilled out of a solid sphere of radius 5 inches.

Radius of sphere = 5 inches

Radius of hole = 2 inches

Volume of sphere =

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

where r is the radius of sphere.

Volume of sphere =

`\displaystyle(4)/(3)\pi (5)^3\\\\=(4)/(3)* 3.14* (5)^3\\\\=523.33\text{ cubic inches}`

Volume of hole =

`\displaystyle(4)/(3)\pi (2)^3\\\\=(4)/(3)* 3.14* (2)^3\\\\=33.49\text{ cubic inches}`

Volume of remaining solid =

Volume of sphere - Volume of hole

`=523.33 - 33.49\\=489.84\text{ cubic inches}`

The volume of remaining sphere is 489.84 cubic inches