Question

Find the volume of the solid enclosed by the paraboloids z=9(x^2+y^2) and z=32-9(x^2+y^2). I keep winding up with 2pi(9-(729/512)), which is incorrect.

Answer 1

How did you do it? Did you use Cyllindrical coordinates?

Answer 2

Ya my integral was:
\[\int\limits_{0}^{2\pi}\int\limits_{0}^{1}(32-9r^2)(rdrd \theta)\]
Which did not get me the right answer.

Answer 3

And why woud that produce the correct answer? You are missing two pieces:

1) Argument: \[(32-9r^{2}) - (9r^{2})\]
2) Limits: \[[0,4/3]\]
You tell me why.

Answer 4

So now my integral would look like:

\[\int\limits_{0}^{2\pi}\int\limits_{0}^{4/3}\int\limits_{9r^2}^{32-9r^2}rdzdrd \theta\]

Correct?

Answer 5

Thanks I got it.

Answer 6

Where did "4/3" come from? You need to demonstrate that you can find that on your own.