Question: A rectangle with a perimeter of 40cm is rotated around one of its sides, creating a right cylinder. What is the largest possible volume for this cylinder?(adsbygoogle = window.adsbygoogle || []).push({});

Here's what I have done so far:

Equation #1:

40 = 2h + 2r

r = 20 - h

Equation #2:

Volume = pi*r^2h

= pi(20-h)(h)

= 20pi*h - h^2*(pi)

Derivate of volume: 20pi-2pi*h

10=h

Therefore, r also equals 10.

Thus, the maximum volume is 3141.592cm^3, which is incorrect.

The actual answer is 3723.37cm^3. Any help would be great.

Sorry, but I think this should be in the "Calculus and Beyond" board.

I'm not too sure how to move it there, though.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Simple word problem.

**Physics Forums | Science Articles, Homework Help, Discussion**