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=(1)/(4)h`. We sub that value for r into the formula and we get the volume in terms of height only.
`V=\pi ((1)/(4)h)^2h` and
`V=(1)/(16)\pi h^3`. Solving that for the height gives us
`h^3=(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.