# 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:

## Answers and Replies

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

Dick
Science Advisor
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
Science Advisor
Homework Helper
That's only true along the curve where the two cylinders intersect. It's not true everywhere on the surface in the first octant.

That's only true along the curve where the two cylinders intersect. It's not true everywhere on the surface in the first octant.

Thanks Thanks Thanks