Final answer:
The volume of the Earth is approximately 1.083 x 10^21 times larger than the volume of a ping-pong ball.
Step-by-step explanation:
To find the ratio of the volumes, we need to compare the volume of the Earth to the volume of a ping-pong ball. The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius.
For the Earth, the radius is 3,960 miles. Converting this to inches, we get 3,960 miles × 5,280 feet/mile × 12 inches/foot = 251,136,000 inches.
For the ping-pong ball, the radius is 0.7441 inches. Substituting the values into the volume formula, we get:
Volume of Earth = (4/3)π(251,136,000)^3
Volume of ping-pong ball = (4/3)π(0.7441)^3
Therefore, the volume of the Earth is:
Volume of Earth/Volume of ping-pong ball = [(4/3)π(251,136,000)^3] / [(4/3)π(0.7441)^3]
After simplifying and canceling out terms, we get:
Volume of Earth/Volume of ping-pong ball = (251,136,000)^3 / (0.7441)^3
Calculating this expression gives approximately 1.083 × 10^21. So, the volume of the Earth is about 1.083 × 10^21 times larger than the volume of a ping-pong ball.