Explanation Given: The solid whose base is the region enclosed by y = x 2 and y = 3 and cross section perpendicular to y -axis is rectangle of height y 3 . Calculation: For each y, the distance to the parabola from the y -axis is y . Therefore, the side(s) length of the rectangle is given by; ⇒ s = 2 y So, the area of cross section (let us consider, A) of rectangle is given by; ⇒ A = b a s e ( b ) × h e i g h t ( h ) = ( 2 y × y 3 ) ( ∵ b = 2 y , h = y 3 ) ∴ A = 2 y 7 2 Finally, the volume

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.2, Problem 14E

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Find the volume $V$ of solid whose base is the region enclosed by $y = x^{2}$ and $y = 3$ . The cross section perpendicular to $y$ -axis is rectangle of height $y^{3}$ .

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Chapter 6.2, Problem 13E

Chapter 6.2, Problem 15E

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Chapter 6 Solutions

Calculus - Standalone book

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - 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Find the volume V of solid whose base is the region enclosed by y = x 2 and y = 3 . The cross section perpendicular to y -axis is rectangle of height y 3 .

Solution Summary: The author explains how to determine the volume V of a solid, whose base is the region enclosed by y = x 2.

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Find the volume $V$ of solid whose base is the region enclosed by $y = x^{2}$ and $y = 3$ . The cross section perpendicular to $y$ -axis is rectangle of height $y^{3}$ .

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Chapter 6 Solutions

Find the volume V of solid whose base is the region enclosed by y = x 2 and y = 3 . The cross section perpendicular to y -axis is rectangle of height y 3 .

Solution Summary: The author explains how to determine the volume V of a solid, whose base is the region enclosed by y = x 2.

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Find the volume V of solid whose base is the region enclosed by y=x2 and y=3. The cross section perpendicular to y-axis is rectangle of height y3.

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Chapter 6 Solutions

Find the volume $V$ of solid whose base is the region enclosed by $y = x^{2}$ and $y = 3$ . The cross section perpendicular to $y$ -axis is rectangle of height $y^{3}$ .