# calculus

posted by .

A cylindrical container is to hold 20π cm^3. The top and bottom are made of a material that costs \$0.40 per cm^2. The material for the curved side costs \$0.32 per cm^2.

Find the height in centimeters of the most economical container.

• calculus -

let the height be h

V = πr^2 h
πr^2 h = 20π
h = 20/r^2

Cost = .40(2πr^2) + .32(2πrh)
C = .8πr^2 + .64πr(20/r^2)
= .8πr^2 + 12.8π/r
dC/dr = 1.6πr - 12.8π/r^2
= 0 for a min of C

1.6πr = 12.8π/r^2
1.6r^3 = 12.8
r^3 = 8
r = 2
then h = 20/4 = 5

the cylinder should be 5 cm high and have a radius of 2 cm.

## Similar Questions

1. ### Calculus

The top and bottom of a can must be made of copper that costs two cents per square inch and the curved side is to be made of aluminum that costs one cent per square inch. Find the radius and height of the can that will maximize the …

A cylindrical can is to hold 20 pie mraised to the 3rd power. The material for the top and bottom costs \$10/m raised to the 2nd power and material for the side costs \$8/m to the 2nd power. Find the radius r and height h of the most …
3. ### Math

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 …
4. ### 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 …
5. ### 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
6. ### 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 …
7. ### Calculus

A manufacturer needs to produce a cylindrical can with a volume (capacity) of 1000cm cubed. The top and the bottom of the container are made of material that costs \$0.05 per square cm, while the side of the container is made of material …
8. ### Calculus

A manufacturer needs to produce a cylindrical can with a volume (capacity) of 1000cm cubed. The top and the bottom of the container are made of material that costs \$0.05 per square cm, while the side of the container is made of material …
9. ### Calculus

A rectangular storage container with an open top is to have a volume of 10 . The length of its base is twice the width. Material for the base costs \$12 per square meter. Material for the sides costs \$5 per square meter. Find the cost …
10. ### help meee

A cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and …

More Similar Questions