If the volume of a cylindrical block is equal to 800cm^3 prove that the total surface area is equal to 2(pi)x^2 + (1600)/x, where x cm is the radius of the base. hence obtain the value x which makes the surface area a minimum.

Answer 1

πx^2 h = 800
h = 800/(πx^2)

The area is two circles plus a curved cylinder, so
a = 2πx^2 + 2πxh

the result follows, so just find x such that da/dx = 0