Question

If the radius of the Earth is roughly 3,960 miles, how many times larger is the volume of the Earth than the volume of a ping-pong ball? A ping-pong ball has a radius of 0.7441 inches. 1 mile = 5,280 feet.

Answer 1

1) we calculate the volume of the Earth expressed in ft.
Volume of a sphere=(4/3)πr³
3960 miles=3960 miles*(5280 ft/1 mile)=20908800 ft

Volume of the Earth=(4/3)π(20908800 ft)³=(4/3)9.1408*10²¹π ft³

2) we calculate the volume of a ping-pong ball at miles

V=(4/3)π(0.7441 in)³=(4/3)0.412π in³

3)we calculate how many times larger is the volume of the Earh tan the volume of a ping-pòng ball.

(4/3)0.412π in³------------------------ a ping-pong ball.
(4/3)9.1408*10²¹π ft³-------------- x

x=(4/3)9.1408*10²¹π ft³* volume of a ping-pong ball) /(4/3)0.412π in³)=
=2.21865*10²² ping-pong balls.

Answer: The volume of the Earth is 2.21865*10²² times larger than the volume of a ping-pong ball.