# Finding Volume by use of Triple Integrals

1. Apr 12, 2013

1. The problem statement, all variables and given/known data
Find the Volume of the solid eclose by y=x$^{2}$+z$^{2}$ and y=8-x$^{2}$-z$^{2}$

3. The attempt at a solution

Well know they're both elliptic paraboloids except one is flipped on the xz-plane and moved up 8 units. Knowing this, i equated the two equations and got 4=x$^{x}$+z$^{2}$ which is the Domain of this volume.

I found the limits of the intergration..... x$^{2}$+z$^{2}$$\leq$y$\leq$8-x$^{2}$-z$^{2}$......-$\sqrt{y-z^{2}}$$\leq$x$\leq$$\sqrt{y-z^{2}}$.....-2$\leq$z$\leq$2

But my problem now is what am i actually integrating. would it be x$^{2}$+z$^{2}$?

Last edited by a moderator: Apr 12, 2013
2. Apr 12, 2013

### LCKurtz

No. The integrand would be $1$.$$Vol = \iiint_R 1\, dV$$And I would suggest you using polar coordinates in the $xz$ plane after you do the $dy$ integral.