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

Volume of a sphere = \(\large \frac 43 \pi r^3\)
\[
\frac{\text{Volume of Earth}}{\text{Volume of ping-pong ball}}
=\large \frac{\frac 43 \pi r_e^3}{\frac 43 \pi r_p^3} = \frac{r_e^3}{r_p^3} \\
r_e = \text{Radius of the Earth} = 3960 \times 5280 \times 12 ~\text{inches.} \\
r_p = \text{Radius of the ping-pong ball} = 0.7441 ~\text{inch.}
\]Plug in the numbers and calculate the ratio.