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

Answer:

The volume of remaining sphere is 489.84 cubic inches.

Step-by-step 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 =

$\dfrac{4}{3}\pi r^3$

where r is the radius of sphere.

Volume of sphere =

$\displaystyle\frac{4}{3}\pi (5)^3\\\\=\frac{4}{3}\times 3.14\times (5)^3\\\\=523.33\text{ cubic inches}$

Volume of hole =

$\displaystyle\frac{4}{3}\pi (2)^3\\\\=\frac{4}{3}\times 3.14\times (2)^3\\\\=33.49\text{ cubic inches}$

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