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.

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