SOLUTION: For a closed cylinder with radius r ⁢ cm and height h ⁢ cm, find the dimensions giving the minimum surface area, given that the volume is 28 cm3. Enter the exact ans

Algebra ->  Equations -> SOLUTION: For a closed cylinder with radius r ⁢ cm and height h ⁢ cm, find the dimensions giving the minimum surface area, given that the volume is 28 cm3. Enter the exact ans      Log On


   

Question 1069401: For a closed cylinder with radius r ⁢ cm and height h ⁢ cm, find the dimensions giving the minimum surface area, given that the volume is 28 cm3.
Enter the exact answers.
I have r
but I have no clue how to get h
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28h%2Api%2Ar%5E2=28%2Cs=surfaceArea%2Cs=h%2A2pi%2Ar%2B2%2Api%2Ar%5E2%29

You are interested in finding the minimum s.
You said, you have r, but want h. Use your volume equation. You can find r in terms of h, or you can find h in terms of r. It is your choice which you choose. You want s as a function of one variable.

h=28%2F%28pi%2Ar%5E2%29

s=%2828%2F%28pi%2Ar%5E2%29%292pi%2Ar%2B2%2Api%2Ar%5E2-----simplify this.