Question

A cylindrical can, open at the top, is to hold 500 cm3 of liquid. Find the height and radius that minimize the amount of material needed to manufacture the can.

Answer 1

Height = h
Radius = r

Volume = 500 = h×(pi)r²
SA = 2(pi)r² + 2(pi)rh

Where I would start:
\[h=\frac{ 500}{ \pi r^2 }\]