Triple Integral: Volume of a Solid

[iamalexalright]

Homework Statement

Been awhile since I've done them and my memory/reasoning isn't so great apparently...

Use the triple integral to find the volume of the given solid:
The solid enclosed by the cylinder
$$x^{2} + y^{2} = 9$$
and the planes y + z = 16 and z = 1. 2. The attempt at a solution
Difficulty is always setting up the bounds of the integral...
$$-3 \leq y \leq 3$$
$$1 \leq z \leq 16 - y$$
having problems with the xwould it be:
$$-\sqrt{9 - y^{2}} \leq x \leq \sqrt{9 - y^{2}}$$ ?

 

[Dick]

Sure. The planes don't intersect inside the cylinder. So you can parametrize the integral over the x,y in the circle defining the cylinder without worrying about the z value. If the planes had intersected inside the circle they would have had to give you a more elaborate description of the region.

 

[iamalexalright]

135*pi, cool! Thanks Dick

 

[Dick]

135*pi, cool! Thanks Dick

That's what I get. :)