How do we describe the region of integration of the proposed triple integral?

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When finding the volume outside the cylinder $x^2+y^2=25$ and inside the sphere $x^2+y^2+z^2=100$, the bounds are: $0 \leq \theta \leq 2\pi$ and $5 \leq r \leq 10$

What are the bounds for $z$?

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What is the intersection of the cylinder $x^{2} + y^{2} = 25$ and the sphere $x^{2} + y^{2} + z^{2} = 100$?