Use double integral to find the volume

[zhuyilun]

Homework Statement

bounded by x^2+y^2=r^2 and y^2 +z^2=r^2
i guess r is just a random constant

Homework Equations

The Attempt at a Solution

i don't even have a clue of how to start this question

 

[LCKurtz]

I have posted a "freehand" picture to get you started. The picture shows the intersection of the cylinders in the first octant so it represents 1/8th of the volume. You will want to use a yz integral. I have oriented it so to make it "easier" to see.

[EDIT] Corrected mis-labeling of axes, use an xz integral

 

[PhaseShifter]

Actually that illustration is for x²+y²=r² and x²+z²=r².

Not a huge deal though, since it gives the same numerical answer either way. Just rotate the axis labels one place in the clockwise direction and use an xz integral.