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