A soup company wants to manufacture a can in the shapeof a right circular cylinder that

Chapter 0, Problem 33

(choose chapter or problem)

A soup company wants to manufacture a can in the shape of a right circular cylinder that will hold \(500 \mathrm{~cm}^{3}\) of liquid. The material for the top and bottom costs \(0.02 \mathrm{cent} / \mathrm{cm}^{2}\), and the material for the sides costs \(0.01 \mathrm{cent} / \mathrm{cm}^{2}\).

(a) Estimate the radius \(r\) and the height \(h\) of the can that costs the least to manufacture. [Suggestion: Express the cost \(C\) in terms of \(r\).]

(b) Suppose that the tops and bottoms of radius \(r\) are punched out from square sheets with sides of length \(2r\) and the scraps are waste. If you allow for the cost of the waste, would you expect the can of least cost to be taller or shorter than the one in part (a)? Explain.

(c) Estimate the radius, height, and cost of the can in part (b), and determine whether your conjecture was correct.

Equation Transcription:

Text Transcription:

500 cm^3

0.02 cent/cm^2

0.01 cent/cm^2

r

h

C

r

r

2r