Question

Ryan wants to use the Fermi process to estimate the number of basketballs that would fill a gymnasium. As part of the process, he needs to estimate the volume of a basketball. The diameter of a basketball is about 10 in. 
Which estimate best approximates the volume of a basketball? 5×10^1 in³ 
5×10^2 in³
5×10^3 in³ 
5×10^4 in³

Answer 1

A basketball is the shape of a sphere.

The volume of a sphere is given by

$V= \frac{4}{3} \pi r^3$

Given that the diameter of the basketball is 10 in., thus the radius is 10 / 2 = 5 in.

Thus, the volume of the basketball is given by

$V= \frac{4}{3} \pi(5)^3 \\ \\ = \frac{4\times125}{3} \pi=523.6\ in^3$

Therefore, The best approximate of the volume of the basketball is $5\times10^2\ in^3$