Volume of three shared cylinders

[physics_freak]

Homework Statement

Calculate the volume of the space enclosed by three cylinders x²+y²=1, x²+z²=1, and y²+z²=1.

Homework Equations

Triple Integral.

The Attempt at a Solution

change to polar coordinates

 

[Dick]

If x^2+z^2=1 and y^2+z^2=1 then x^2=y^2=1-z^2. The cross sections of your surface are squares integrating dz. I definitely wouldn't change to polar coordinates.

 

[physics_freak]

What is the range of z if I integrate w.r.t z?

 

[Dick]

What is the range of z if I integrate w.r.t z?

What's the range of z on the curve x^2+z^2=1?

 

[physics_freak]

is it (+/-) sqrt of 1-x^2?

 

[Dick]

is it (+/-) sqrt of 1-x^2?

Those are the values for single value of x. Suppose you consider all possible x?