use triple integration to find the volume of the area inside the sphere x2+y2+z2=4z but outside the sphere x2+y2+z2=4. its urgent pls

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- Jan 6th 2009, 03:41 AMcorrecttriple integration
use triple integration to find the volume of the area inside the sphere x2+y2+z2=4z but outside the sphere x2+y2+z2=4. its urgent pls

- Jan 6th 2009, 04:51 AMmr fantastic
- Jan 6th 2009, 05:37 AMcorrect
thank you. pls what should i do next

- Jan 6th 2009, 05:40 AMJester
- Jan 6th 2009, 07:30 AMcorrect
i don't know how to proceed

- Jan 7th 2009, 07:03 AMmr fantastic
- Jan 7th 2009, 11:49 AMcorrect
i know its triple integral dxdydz transforming this to polar coordinates it becomes r2sinthetadthetadpsi. if i use this, i don't know the limits

- Jan 7th 2009, 08:19 PMmr fantasticQuote:

to find the volume of the area inside the sphere x2+y2+z2=4z but outside the sphere x2+y2+z2=4.

To get the enclosed volume:

First draw a simple diagram diagram. Looking at it side-one in the xz-plane (y = 0) it's not hard to see that the top surface is and the bottom surface is . This supplies the z-integration terminals.

The x and y integration terminals define the region in the xy-plane defined by the circle .

So integrate the triple integral first with respect to z and then switch to polar coordinates. - Jan 8th 2009, 01:27 AMDeMath