Math
posted by jonh .
A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.06 cents per square centimeter. Find the dimensions for the can that will minimize production cost.

let the radius be r
let the height be h
Volume = πr^2h
πr^2h = 400
h = 400/(πr^2)
cost = different prices x surface areas
= .03(2πrh) + 2(.06) πr^2
= .03[2πr(400/πr^2) + 4πr^2]
= .03[ 800/r + 4πr^2]
d(cost)/dr = .03[ 800/r^2 + 8πr] = 0 for a min of cost
800/r^2 = 8πr
100/π = r^3
r = 3.169
h = 400/(π(3.169)^2) = 12.679
check my arithmetic
Respond to this Question
Similar Questions

Calculus
A right cicular cylindrical can is to be constructed to have a volume of 57.749 cubic inches (one quart). The sides of the can are to be formed by rolling and welding a strip of metal, which may be purchased in rolls with width equal … 
math
A right cicular cylindrical can is to be constructed to have a volume of 57.749 cubic inches (one quart). The sides of the can are to be formed by rolling and welding a strip of metal, which may be purchased in rolls with width equal … 
math
A right cicular cylindrical can is to be constructed to have a volume of 57.749 cubic inches (one quart). The sides of the can are to be formed by rolling and welding a strip of metal, which may be purchased in rolls with width equal … 
calculus
a rectangular box is to have a square base and a volume of 20 ft cubic if the material for the base costs 30 cent per square foot, the material for the sides cost 10 cent per sqaure foot, and the material for the top costs 20 cents … 
Math (algebra)
Could you help me with this math question: A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of material that costs 11 cents per square centimeter, while … 
Math
A rectangular box is to have a square base and volume of 78 feet cubed. If the material for the base costs $.30 per square feet, the material for the sides costs $.10 per square foot, and the material for the top costs $.20 per square … 
math algebra
Can someone help me with this question? A can in the shape of a right circular cylinder is required to have a volume of 1,000 cubic centimeters. The top and bottom are made up of a material that costs 10ยข per square centimeter, while 
Pre Calculus
A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0.02 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and … 
Calculus
A box with square base and rectangular sides is being designed. The material for the sides costs 20 cents per square inch and that for the too and bottom costs 10 cents per square inch. The box is to hold 150 cubic inches. What dimension … 
math
A microwaveable cupofsoup package needs to be constructed in the shape of cylinder to hold 550 cubic centimeters of soup. The sides and bottom of the container will be made of syrofoam costing 0.03 cents per square centimeter. The …