- #1
danizh
- 16
- 0
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.
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.