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? 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.