# Double Integration to Find Volume

1. Nov 10, 2007

### doppelganger007

1. The problem statement, all variables and given/known data

Find the volume of the region inside the surface z=x^2+y^2 and between z=0 and z=10

2. Relevant equations

x^2+y^2=10

3. The attempt at a solution

I know that I have to use some sort of double integration to find this volume, but I'm not really sure where to begin with the problem

2. Nov 10, 2007

### Kummer

$$\iiint_V dV$$ the upper curve is $$z=10$$ the lower curve is $$z=0$$ the area of integration in $$\mathbb{R}^2$$ is a circle of radius 10. Now use cyclindrical change of variable.

3. Nov 10, 2007

### doppelganger007

hmm...I may try that if I can't find an alternative, but is there any way to do this problem with a double integration and not a triple integration? because the section i'm working with is strictly double integration

4. Nov 11, 2007

### HallsofIvy

That's a paraboloid. Since you have "flat" bottom and top I recommend you imagine the solid consisting of thin horizontal pieces. It should be obvious that the piece at height z is a disk satisfying $x^2+ y^2= z$. What is the area of that disk? If you think of the disk as having thickness "dz", what is its volume? Now "add" the volumes of all those disks.