I am really having problems with this one

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A cylindrical can with no lid is made from 100cm^2 of metal. Show that the volume of the can is given by V = 50r - (pi* r^3/2) where

r= can's radius

Find the radius that gives the maximum volume. Find the maximum volume.

thanks in advance
 
A cylindrical can with no lid is made from 100cm^2 of metal. Show that the volume of the can is given by V = 50r - (pi* r^3/2) where

r= can's radius

Find the radius that gives the maximum volume. Find the maximum volume.

1--The volume V = Pi(r^2)h.

2--The area = 100 = Pi(r^2) + 2Pi(r)h

3--Solve for h and substitute into (1)

4--Take the first derivitive,, set equal to zero,, and solve for r.

5--Susbtitute r into (1) and solve for h.

6--Compute the volume of the can.
 
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