Question

For a closed cylinder with radius r cm and height h cm, find the dimensions giving the maximum volume, given that the surface area is 50 cm2

Answer 1

\[SA = 2\pi r^{2} + 2\pi rh \]\[50 = 2\pi r^{2} +2 pi r h \]\[h = \frac{ 50-2 \pi r^{2} }{ 2\pi r }\]

Answer 2

\[V = \pi r^{2} h\\V = \pi r^{2} [\frac{ 50 - 2 \pi r^{2} }{ 2\pi r }]\]

Answer 3

Find the maximum r ..\[h'(r) =\frac{d}{dr}(\frac{ 50-2\pi r^{2}}{2 \pi r })\]

Answer 4

Solve for h.