Question

A craftsman wants to make a cylindrical jewelry box that has volume, V, equal to 60 cubic inches.
He will make the base and side of the box out of a metal that costs 50 cents per square inch. The lid of the box will be made from a metal with a more ornate finish which costs 150 cents per square inch.
-Rewrite your expression for the cost of the box in terms of the single variable r.
-Differentiate C with respect to r, to find the derivative dC / dr.
-Find the value of r for which we have a potential relative extreme point of C.
-What is the height of the box?

Answer 1

Volume:
V = pi*r^2*h = 60

h = 60/(pi*r^2)

Area:
Area of lid = pi*r^2
Area of Curved area + bottom = pi^r^2 + 2pi*r*h

Put the h we worked out in terms of r into the area equation.

Cost = 0.50*(pi*r^2) + 1.50*(pi^r^2 + 2pi*r*[60/(pi*r^2)]

Tidy up a little and then differenciate and put equal to zero (0 is the slope of the tangent to the graph where the maximum/minimum points occur)

See how you get on from there.

Answer 2

typo in the curved area.
Sould be pi*r^2 not pi^r^2
Same in the cost equation