1. ## Optimization Problem 2

A cylindrical metal can is made to hold 500 mL of soup. Determine the dimensions of the can that will minimize the amount of metal required. Assume that the top and sides of the can are made from metal of the same thickness.

I need help with finding the domain of the r value.

I have

rE(0, ?]

How would I find the largest r value? I know that the largest value occurs when h is the smallest. The height.. could it be 0? But then this doesn't make sense:
V=500
500=pi r ^2 h
so if h = 0 then it cancels out r, and I can't find the largest value of r.

2. Originally Posted by john-1
A cylindrical metal can is made to hold 500 mL of soup. Determine the dimensions of the can that will minimize the amount of metal required. Assume that the top and sides of the can are made from metal of the same thickness.

I need help with finding the domain of the r value.

I have

rE(0, ?]

How would I find the largest r value? I know that the largest value occurs when h is the smallest. The height.. could it be 0? But then this doesn't make sense:
V=500
500=pi r ^2 h
so if h = 0 then it cancels out r, and I can't find the largest value of r.