Calculating volume using triple integrals

1. Mar 1, 2012

kikifast4u

1. The problem statement, all variables and given/known data
Find the volume of the solid enclosed between the cylinder x2+y2=9 and planes z=1 and x+z=5

2. Relevant equations
V=∫∫∫dz dy dz

3. The attempt at a solution
The problem I have here is setting the integration limits. I first tried using:
• z from 1 to 5-x
• y from √(9-x2) to -3
• x from -3 to 3

However, that gave me a negative answer, so I doubt that's the way to do it.

I then used polar coordinates for x and y and used the integral:
V=∫∫∫r dz dr dθ with limits
• z from 1 to 5-r*cos(θ)
• r from 0 to 3
• θ from 0 to 2∏

This time I got a positive answer, but I'm not sure whether the method is correct. We were never taught to use polar coordinates in volume integrals, so I'm not sure whether it's fine to mix them up.

2. Mar 3, 2012

kikifast4u

I'm still struggling with this. Any help guys?

3. Mar 3, 2012

HallsofIvy

Staff Emeritus

• Okay, that's good.

Why -3? The cylinder x2+ y2= 9 goes from $-\sqrt{9- x^2}$ to $\sqrt{9- x^2}$.

4. Mar 3, 2012

kikifast4u

Thank you very much! I got the same answer as in the second method, so both are fine. Stupid stupid mistake!