# Help finding the cost function?

• Oct 12th 2010, 10:41 PM
yess
Help finding the cost function?
A cylindrical can holds 400cm^3 of liquid. The cost of material for the circular top and bottom of the can is 3 cents per square centimeter and the cost of material for the curved sides is 2 cents per square centimeter. Find two equations for the cost C in terms of...
a) the radius of the top and bottom
b) the height of the can h

soo i know v= (pi)r^2(h) but i don't know how that helps me at all in this problem!
• Oct 13th 2010, 03:44 AM
HallsofIvy
You also need to know that the area of the top and bottom, each, is $\displaystyle \pi r^2$ and the area of the curved side is the area of the rectangle having width equal to the height of the can, h, and length equal to the circumference of the circular base (imagine cutting the curved side of the can down its length and flattening it), $\displaystyle 2\pi r$ and so is $\displaystyle 2\pi rh$. Multiply each of those three areas by its cost and add to find the total cost in terms of the two variables, r and h.

Since $\displaystyle V= \pi r^2h= 400$, you can solve that for either r in terms of h or h in terms of r. In the equation for cost, replace, in (a), h by its formula in terms of r and, in (b), r by its formula in terms of h.