Question

An exercise ball contains 4000 cubic inches of air when fully inflated. Write and graph a cubic function to model this situation. Use your graph to estimate the radius of the ball.

Answer 1

Answer:

r = 9.8475 in

Step-by-step explanation:

We assume that the ball is spherical.

The volume of a spherical ball is:

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

We know that:

$V = 4000in ^ 3\\4000 = \frac{4}{3}\pi r ^ 3$

Then

$r ^ 3 = \frac{3*4000}{4(\pi)}\\\\r = \sqrt[3]{\frac{3*4000}{4(\pi)}}\\\\r = 9.8475in$

Below is the graph of the cubic function