Finding volume using triple integral

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To find the volume of the solid defined by the equations x^2+y^2 > 1, x^2+z^2 = 1, and x^2+y^2 = 1, a triple integral approach is necessary, using the integrand of 1. The integration should be set up in cylindrical coordinates, specifically using dz, r, and dθ. The suggested limits for z are from 0 to sqrt(1 - cos^2(θ)) and from 0 to sqrt(1 - sin^2(θ)). The volume calculation focuses on the first quadrant, with the final result being multiplied by 8 to account for symmetry. Reevaluating the coordinate system may provide a clearer path to the solution.
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Homework Statement



I need to find the volume of a solid formed by the following equations:
x^2+y^2 > 1
x^2+z^2 = 1
x^2 + y^2 =1

The Attempt at a Solution



I know that it is a triple integral and the integrand is 1.
I also know that I need to use dzrdrd\theta.

I believe that you need two integrals, one with z going from 0 to sqrt (1-costheta^2) and the other with z going from 0 to sqrt (1-sintheta^2). I only want to find the volume in the first quadrant then I will multiply by 8.
 
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Have you been told you need to use dz rd rd\theta ?

If so then rethink you co-ordinate system when integrating, and look at your functions and see if you can convert them into any other coordinate system you know of
 

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