SOLUTION: Several cylinders are different sizes, but for each one the surface area and the volume have the same numerical value. If the radius and height are both integers, what is the large

Algebra ->  Surface-area -> SOLUTION: Several cylinders are different sizes, but for each one the surface area and the volume have the same numerical value. If the radius and height are both integers, what is the large      Log On


   

Question 1006528: Several cylinders are different sizes, but for each one the surface area and the volume have the same numerical value. If the radius and height are both integers, what is the largest volume possible?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Several cylinders are different sizes, but for each one the surface area and the volume have the same numerical value.
If the radius and height are both integers, what is the largest volume possible?
:
Assuming the Surface area includes the ends.
:
Surface area = volume
%282%2Api%2Ar%5E2%29+%2B+%282%2Api%2Ar%2Ah%29+=+pi%2Ar%5E2%2Ah
factor out pi*r
pi%2Ar%282r+%2B+2h%29+=+pi%2Ar%5E2%2Ah
divide both sides by pi*r
2r + 2h = rh
2r = rh - 2h
factor out h
2r = h(r-2)
Divide both sides by (r-2) and write
h = %282r%29%2F%28r-2%29
:
Looking at this simple equation, we can see that r has to be greater than 2
Try:
r = 3, then h = 6
r = 4, then h = 4
r = 5, h is not an integer
r = 6, h = 3
no other integer solutions
Max volume: r=6; h=3; pi%2A6%5E2%2A3 = 339.3 cubic units
:
:
Check solution by finding the surface area where r=6; h=3
%282%2Api%2Ar%5E2%29+%2B+%282%2Api%2Ar%2Ah%29 = 339.3 sq units