9th Edition

ISBN: 9781337613927

Author: Stewart

Publisher: CENGAGE L

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Chapter 6, Problem 4PP

A cylindrical glass of radius r and height L is filled with water and then tilted until the water remaining in the glass exactly covers its base.

(a) Determine a way to “slice” the water into parallel rectangular cross-sections and then set up a definite integral for the volume of the water in the glass.

(b) Determine a way to “slice” the water into parallel cross-sections that are trapezoids and then set up a definite integral for the volume of the water.

(d) Find the volume of the water in the glass from purely geometric considerations.

(e) Suppose the glass is tilted until the water exactly covers half the base. In what direction can you “slice” the water into triangular cross-sections? Rectangular cross-sections? Cross-sections that are segments of circles? Find the volume of water in the glass.

Chapter 6, Problem 4PP, A cylindrical glass of radius r and height L is filled with water and then tilted until the water

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Calculus, Early Transcendentals

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Solution Summary: The author explains how to "slice" the water into parallel rectangular cross-sections, and sets up a definite integral for the volume of water in the glass.

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