Minimum amount of material for a cylinder

Question

A cylinder storage tank holds 1900 ft³ of gasoline. Determine the minimum amount of material needed to build this tank. Start by stating the dimensions of a cylinder that will allow for minimum material

Answer 1

V = πr²h

1900 = πr²h

1900 / (πr²) = h

T.A. = 2π² + 2πrh

T.A. = 2πr² + 2πr(1900 / πr²)

Differentiate and set equal to zero.