Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.1 Areas and Volumes by Slices, #66 · Calculus · Applications of integrals

A horizontal slice of the sphere-with-hole in Figure 8.6b is a washer

A horizontal slice of the sphere-with-hole in Figure 8.6b is a washer. Its area is $π x^{2} - π a^{2} = π (b^{2} - y^{2} - a^{2})$ .
(a) Find the upper limit on $y$ (the top of the hole).
(b) Integrate the area to verify the volume in Example 12.

This exercise builds on another exercise in its source book, which isn't shown here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.1 Areas and Volumes by Slices, #66

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