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

The bottle is a cylinder, height h radius r=h/4.

$V = \pi r^2 h = \pi (h/4)^2 h = \frac{\pi}{16} h^3$

$h^3 = \dfrac{16V}{\pi}$

$h = \sqrt[3]{ \dfrac{16V}{\pi} }$

Answer: second choice, cube root