express the surface of a right circular cylinder a function of its volume assuming the height is constant
Let the height be h (constant).
First find radius in terms of V, volume.
Volume, V = πr²h
radius, r = √(V/(πh))
So the total surface area is obtained by substituting r in the following expression:
A(total)
=2πrh+2πr^2
=2π√(V/(πh))(√(V/(πh))+h)
which simplifies to
2√(V/h)*(√(V/h)+√(π)h)