The surface area of a cylindrical can is equal to the sum of the area of two circles and the body of the cylinder: 2πr2 + 2πrh. volume is equal to πr2h.
V = πr2h = 128 pi
r2h = 128
h = 128/r2
A = 2πr2 + 2πrh
A = 2πr2 + 2πr*(128/r2)
A = 2πr2 + 256 π / r
the optimum dimensions is determined by taking the first derivative and equating to zero.
dA = 4 πr - 256 π /r2 = 0
r = 4 cm
h = 8 cm
