Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.1 Areas and Volumes by Slices, #68 · Calculus · Applications of integrals

An upright cylinder of radius … is sliced by two parallel planes…

An upright cylinder of radius $r$ is sliced by two parallel planes at angle $α$ . One is a height $h$ above the other.
(a) Draw a picture to show that the volume between the planes is $π r^{2} h$ .
(b) Tilt the picture by $α$ , so the base and top are flat. What is the shape of the base? What is its area $A$ ? What is the height $H$ of the tilted cylinder?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.1 Areas and Volumes by Slices, #68

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