Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.1 Areas and Volumes by Slices, #41 · Calculus · Applications of integrals

**The slices in 43–46 are washers

A cylinder of radius $r$ and height $h$ is half full of water. Tilt it so the water just covers the base.

(a) Find the volume of water by common sense.

(b) Slices perpendicular to the $x$ axis are (rectangles) (trapezoids) (curved). I had to tilt an actual glass.

### *42
Find the area of a slice in Problem 41. (The tilt angle has $tan θ = 2 h / r$ .) Integrate to find the volume of water.

The slices in 43–46 are washers. Find the slice area and volume.

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, #41

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