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

r = 9.8475 in

Explanation:

We assume that the ball is spherical.

The volume of a spherical ball is:

`V = (4)/(3)\pi r ^ 3`

We know that:

`V = 4000in ^ 3\\4000 = (4)/(3)\pi r ^ 3`

Then

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

Below is the graph of the cubic function