Posted by **zeina** on Tuesday, December 28, 2010 at 10:21am.

A cylindrical can is to be made to hold 100cm cubic.The material for its top and bottom cost twice as much per cm square as that for its side.

The objective of this problem is to find the radius and the height of this cylinder such that its cost is minimized.Denote the radius of this can by r and its height by h. Let k be the cost,expressed in cents,of 1 cm square of the side of this can.

1)Express the cost of the side and that two bases in terms of r, h and k.

2)Express the total cost of manufacturing this can in terms of r only.

3)Find r that minimizes the cost.

4)Deduce the corresponding h.

- calculus -
**bobpursley**, Tuesday, December 28, 2010 at 11:20am
Let r be the radius, h the height.

Cost=2K(2PIr^2)+ k*h*PI*(2r)

I will be happy to critique your work on this. A most excellent problem.

- calculus -
**Reiny**, Tuesday, December 28, 2010 at 11:21am
we know volume = πr^2h = 100

h = 100/(πr^2)

k = 2(2πr^2) + 1(2πrh)

= 4πr^2 = 2πr(100/(πr^2))

= = 4πr^2 + 200/r

dk/dr = 8πr - 200/r^2 = 0 for a max/min of k

8πr = 200/r^2

r^3 = 200/(8π)

take it from here

## Answer this Question

## Related Questions

- calculus - A cylindrical container is to hold 20π cm^3. The top and bottom ...
- calculus - a company is designing shipping crated and wants the volume of each ...
- Math (algebra) - Could you help me with this math question: A can in the shape ...
- Calculus - A company is designing shipping crates and wants the volume of each ...
- Math - A cylinder shaped can needs to be constructed to hold 400 cubic ...
- pre-calculus - A company plans to manufacture a container having the shape of a ...
- calculus - a closed box with square base is to have a V= 2000in^3. The material ...
- Calculus - A rectangular box with square base (which is NOT necessarily a cube) ...
- Calculus - A cylindrical drum is made to hold exactly 1m^3 in its interior. ...
- Calculus - An open top box with a square base is to be made so that it holds 3 ...

More Related Questions