A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup.

Question

A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material for the sides of the can costs 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.08 cents per square centimeter. Find the dimensions for the can that will minimize production cost.

Helpful information:

h : height of can, r : radius of can

Volume of a cylinder: V=πr2h

Area of the sides:  A=2πrh

Area of the top/bottom: A=πr2

To minimize the cost of the can:

Radius of the can:    __

Height of the can:    __

Minimum cost:   ___ cents

Answer 1

TL;DR

radius of can: 3.41 cm

height of can: 13.68 cm

minimum cost: 17.5 cents