Question

find at least 3 possible measures for the height and the radius of a cylinder with a lateral area of 144pi square centimeters. which of your dimensions will give you the largest volume?

Answer 1

The height and radius of cylinder with curved surface area is given by:

$\begin{gathered} 2\pi rh=144\pi \\ rh=72 \end{gathered}$

So the possible combinations can be:

$\begin{gathered} r=9,h=8 \\ r=12,h=6 \\ r=24,h=3 \end{gathered}$

The volumes for each dimension is:

$\begin{gathered} V_1=\pi\times9^2\times8=648\pi \\ V_2=\pi\times12^2\times6=864\pi \\ V_3=\pi\times24^2\times3=1728\pi \end{gathered}$

Hence the maximum volume is when r=24 and h=3.

Therefore it can be concluded if the product of radius and height is known, then the height should be as small as possible to maximize the volume of cylinder.