# Volume of the intersection of two cylinders by polar co-ordinates

Volume of the intersection of two cylinders by cylinderical co-ordinates

## Homework Statement

find Volume of the intersection of two cylinders by cylindrical co-ordinates

## The Attempt at a Solution

IN the attached file I found it's 8(a^3)/3
It should be 16 not 8

#### Attachments

• volume.pdf
20.9 KB · Views: 283
Last edited:

I know that the mistake may be trivial but can anyone give me any comment!!!!!!!1

Dick
Homework Helper
Why do you think the upper limit of the dz integration is r*cos(theta)? Don't you have z=sqrt(a^2-y^2)=sqrt(a^2-r^2*sin(theta)^2)?

Last edited:
Why do you think the upper limit of the dz integration is r*cos(theta)? Don't you have z=sqrt(a^2-y^2)=sqrt(a^2-r^2*sin(theta)^2)?

But in the first octent
x^2 + y^2 = r^2
y^2 + z^2 = r^2

so z=x=rcos(theta)

Isn't it?

Dick