I need to find the volume enclosed by and where

How do I find the bounds? Do I apply spherical coordinates as written?

Printable View

- March 11th 2011, 07:51 PMKillerFinding volume by using triple integral
I need to find the volume enclosed by and where

How do I find the bounds? Do I apply spherical coordinates as written? - March 11th 2011, 07:55 PMProve It
To start with, I expect that you have written the second bound wrongly, since that is the equation of a plane figure, not a solid...

- March 11th 2011, 08:00 PMKiller
I edited the first equation, but what's wrong with the second one?

- March 12th 2011, 12:30 AMProve It
It's a 2 Dimensional object, i.e. a plane figure. How are we supposed to know where along the axis it's supposed to lie?

- March 12th 2011, 02:57 AMtom@ballooncalculus
Assuming the cylinder extends indefinitely up and down the z dimension, we have Viviani's Curve. Doing just the top half, we have z going from 0 (where it 'starts', on the (x,y) plane) up to (where it hits the hemisphere). And we have r going from 0 at the centre (z axis), up to a cos theta i.e. everywhere inside the cylinder. And theta is turning through the x-positive half of the space, i.e. from minus pi/2 to pi/2. So...

Just in case a picture helps to follow through from the inside out, we can start bottom left here, integrating r with respect to z...

http://www.ballooncalculus.org/draw/intMulti/two.png

... where (key in spoiler) ...

__Spoiler__:

Which leaves a couple of blanks to fill. Hope this helps.

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote! - March 12th 2011, 04:21 AMHallsofIvy
- March 12th 2011, 04:24 AMProve It
- March 12th 2011, 10:41 AMHallsofIvy
No, it

**was**stated that this problem was in three dimensions. The fact that there was no restriction put on z meant that it could be anything.