Volume of a Wedge in a Cylinder

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A right circular cylinder is cut by two planes to form a wedge. One plane is perpendicular to the axis of the cylinder (the floor), and the second plane through a diameter makes an angle with the floor. Calculate the volume of the wedge for any angle .

Contributed by: Abe Gadalla (June 2015)
Open content licensed under CC BY-NC-SA



This is based on problem 55, Section 6.2, p. 423 of [1]. It was also addressed by James Stewart in example 9, Section 6.2, p. 452 of [2] and by Edwards and Penney in example 7, Section 6.2, p. 383 of [3].


[1] R. E. Larson, R. P. Hostetler, and B. H. Edwards, Calculus, 5th ed., Lexington, MA: D. C. Heath, 1994.

[2] J. Stewart, Single Variable Calculus: Early Transcendentals, 5th ed., Belmont, CA: Thomson Brooks/Cole, 2003.

[3] C. H. Edwards and D. E. Penney, Calculus, 6th ed., Upper Saddle River, NJ: Prentice Hall, 2002.

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