A craftswoman wants to make a cylindrical jewelry box that has volume, V, equal to 55 cubic inches.

She will make the base and side of the box out of a metal that costs 10 cents per square inch. The lid of the box will be made from a metal with a more ornate finish which costs 100 cents per square inch.

Writing the radius of the cylindrical box as r, and the height of the box as h, calculate the cost, C, in cents, of the metal used to produce the box in terms of h and r.

So I thought it would be something like

$\displaystyle 10+100(2pir^2) + 10(2pirh)$

$\displaystyle 110(2pir^2)+10(2pirh)$

but that doesn't seem to be right. (I did also try it with decimals, as it's in cents)

I'm sure I'm missing something obvious here, maybe someone can help???

EDIT: I figured it out, it was something obvious :I

But now I have a new question!

How do I go about differentiating this?

$\displaystyle 100pir^2+10pir^2+10(2pi(55/(pir^2)))$

I got as far as

$\displaystyle 200pir+20pir$

and thought that the rest would just be +10, but that's not it.