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If S is the solid obtained by intersecting the ball $x^2+y^2+z^2\le4$ and $x^2+z^2\le1$

1) How do I show that S is Jordan measurable? Can I simply say the following: "Clearly S is bounded, and the boundary is a union of smooth curves in $R^3$. Since smooth curves have zero content, the boundary is 0."

2) Also for obtaining the volume of S, I am not sure how to calculate the bounds... Do I need the intersections?

Many thanks!

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