Optimize a cylinder of 500cm^3?

Question

Requires Minimum surface area

Answer 1

Equation of the volume of the cylinder. (x=radius) y=x^2hπ

In this case, the volume of the cylinder is 500cm^3. So, 500=x^2hπ

If you divide π in the both sides, then, 159.154=x^2h

So, if you want to have minimum surface area, x has to be same as h.

Which is 5.4192..

The surface area of the cylinder is, 2x^2π+2xhπ=369.0540297...cm^2

369.05 cm^2 (2dp)