# Setting up a double integral to find the volume

1. Jun 27, 2010

### ahmetbaba

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

Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equation

x2+y2+z2=r2

2. Relevant equations
Not much equations, just setting the integral up, however I have no idea.

3. The attempt at a solution

I know how to approach these problems if there were only 2 variables, but I'm kind of stuck since there are three variables that I have to deal with.

2. Jun 27, 2010

### LCKurtz

Then solve the equation for z, giving one or more functions of two variables.

Is there any obvious symmetry you can use?

3. Jun 27, 2010

### ahmetbaba

how can you solve the equation for z, even then there will be r^2. Help me out with the beginning here please.

4. Jun 27, 2010

### LCKurtz

r is just a constant. Do you recognize what the graph of this is?

5. Jun 27, 2010

### ahmetbaba

do we approach this problem by first saying z=o, then x=o and y=o, integrating all three equations. However the question says to set up a double integration, not a triple integration?

6. Jun 27, 2010

### LCKurtz

No, you don't do that. So I will ask you again:

1. Do you recognize what this surface is?

Then solve it for z to get started. Get z in terms of x and y if you are required to do a double integral.

7. Jun 27, 2010

### ahmetbaba

well it is a sphere, we can say that the center of the sphere passes through (0,0,0) so if we calculate the top half, we can multiply by 2, to get the answer.

z=sqrt(r^2-x^2-y^2)

the limits being -r and r for the first integral, and sqrt(r^2-y^2) and -sqrt(r^2-y^2)

is this correct so far?

8. Jun 28, 2010

### LCKurtz

You have the right idea. You might want to change your dxdy integral to polar coordinates to make it easier. If you do that, you might first change the r in the equation of the sphere to a so you don't confuse it with the r in polar coordinates. Good luck. I'm off to bed.

9. Jun 28, 2010

### gomunkul51

x2+y2+z2=r2 is a sphere..
try using spherical coordinates.
set up a triple integral, and do one integration to get to the double integral :)