Homework Help: Calculus - Optimization

Posted by Nevin on Sunday, June 3, 2012 at 7:55pm.

A cylindrical container with a volume of 3000 cm^3 is constructed from two types of material. The side and bottom of the container cost $0.10/cm^2 and the top of the container costs $0.20/cm^2.

a) Determine the radius and height that will minimize the cost.

b) Determine the ratio of diameter to height.

Could you please help me with these questions please and thank you

Calculus - Optimization - bobpursley, Sunday, June 3, 2012 at 8:28pm
Cost=.10*(pi*r^2+2Pi*r*h)+.20PIr^2

volume= PIr^2h or h= volume/PIr^2
h=3000/(PIr^2)

Put that into the cost function for h.

Then take the derivative of cost with respect to r (dCost/dr), set equal to zero, solve for r.

Answer this Question

Related Questions

geometry - A ball of diameter 20 cm fits exactly inside a cylindrical container...
Geometry - Jake has two similar cylindrical pipes. The radius of the first ...
Calculus - I actually have two questions: 4. An open box is to be made from a ...
optimization - While searching for the minimum of ƒ(x) [x2 (x ...
math - the base of a cylindrical juice container is a circle with diameter 20 cm...
HELP!! OPTIMIZATION CALCULUS - A rectangular storage container with a lid is to...
Calculus optimization - A rectangular storage container with a lid is to have a ...
Honors Geometry - A cylindrical container weighs 36 ounces. Another container ...
calculus - A rectangular box is to be constructed from two different materials. ...
physics - A cylindrical brass container with a base of 80.0 cm^2 and height of ...

For Further Reading

First Name:
School Subject:
Answer: