1. May 6, 2014

### Thepiman12

1. The problem statement, all variables and given/known data

A closed cylinder is required to have a volume of 40m^3 but made with the minimum amount of material. Determine the radius and height the cylinder must have to meet such a requirement.

V= πr^2h

Steps needed:

a) Insert value and transpose for h
b) Then sub into the area formula
c) Then differentiate

2. Relevant equations

V= πr^2h

3. The attempt at a solution

V= πr^2h
40= πr^2h
40/h= πr^2
h=πr^2/40

A= 2πrh+2πr^2 Subbing in h= πr^2/40
A= 2πr(πr^2/40)+2πr^2

2. May 6, 2014

### SammyS

Staff Emeritus

Now you need to do step c.
c) Then differentiate.​
Then a little bit more.

3. May 7, 2014

### Thepiman12

I expanded the brackets and got 2πr^2+80r^-1

And differentiated that to 4πr-80r^-2 Is that correct?

After that how would I go on to find the radius r?

4. May 7, 2014

### SammyS

Staff Emeritus
The answer to that is related to "What is the reason for differentiating?" .

When you solved

V = 2πr2h

for h, you made a mistake.

What you have is actually 1/h .