Question

Chloe is a pharmacist and wants to know the height of a medicine bottle received from a supplier. The supplier informed her that the radius of the medicine bottle is one-fourth its height. Chloe knows that the medicine bottle has a volume of V cubic inches.
Which of the following functions would best model the situation above?

exponential

cube root

step

square root

Answer 1

First we have to determine the volume for the cylinder that is the shape of the medicine bottle. The volume formula for a cylinder is $V=\pi r^2h$. Chloe was told that the radius is 1/4 of the height. That means that $r=\frac{1}{4}h$. We sub that value for r into the formula and we get the volume in terms of height only. $V=\pi (\frac{1}{4}h)^2h$ and $V=\frac{1}{16}\pi h^3$. Solving that for the height gives us $h^3=\frac{16V}{\pi}$. If Chloe wants the height, she needs to "undo" that h-cubed by taking the cubed root. That's your answer...cubed root.

Answer 2

Cube Root, is your final answer.