Explanation Given: The solid whose base is the semicircle y = 9 − x 2 and cross section perpendicular to x -axis is square. Calculation: For each x , the base of the square cross section extends from the semicircle y = 9 − x 2 to the x -axis. Therefore, the side (s) length of the square is given by; ⇒ s = 9 − x 2 So, the area (let us consider, A) of square is given by; ⇒ A = ( s ) 2 = ( 9 − x 2 ) 2 ∴ A = 9 − x 2 Finally, the volume V of the solid is given by; ⇒ V = ∫ − 3 3

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.2, Problem 11E

To determine

Find the volume $V$ of solid whose base is the semicircle $y = \sqrt{9 - x^{2}}$ , where $- 3 \leq x \leq 3$ .The cross section perpendicular to $x$ -axis is square.

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Chapter 6.2, Problem 10E

Chapter 6.2, Problem 12E

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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Prob. 36E Ch. 6.5 - Prob. 37E Ch. 6.5 - Prob. 38E Ch. 6.5 - Prob. 39E Ch. 6.5 - Prob. 40E Ch. 6.5 - Prob. 41E Ch. 6.5 - Prob. 42E Ch. 6.5 - Prob. 43E Ch. 6 - Prob. 1CRE Ch. 6 - Prob. 2CRE Ch. 6 - Prob. 3CRE Ch. 6 - Prob. 4CRE Ch. 6 - Prob. 5CRE Ch. 6 - Prob. 6CRE Ch. 6 - Prob. 7CRE Ch. 6 - Prob. 8CRE Ch. 6 - Prob. 9CRE Ch. 6 - Prob. 10CRE Ch. 6 - Prob. 11CRE Ch. 6 - Prob. 12CRE Ch. 6 - Prob. 13CRE Ch. 6 - Prob. 14CRE Ch. 6 - Prob. 15CRE Ch. 6 - Prob. 16CRE Ch. 6 - Prob. 17CRE Ch. 6 - Prob. 18CRE Ch. 6 - Prob. 19CRE Ch. 6 - Prob. 20CRE Ch. 6 - Prob. 21CRE Ch. 6 - Prob. 22CRE Ch. 6 - Prob. 23CRE Ch. 6 - Prob. 24CRE Ch. 6 - Prob. 25CRE Ch. 6 - Prob. 26CRE Ch. 6 - Prob. 27CRE Ch. 6 - Prob. 28CRE Ch. 6 - Prob. 29CRE Ch. 6 - Prob. 30CRE Ch. 6 - Prob. 31CRE Ch. 6 - Prob. 32CRE Ch. 6 - Prob. 33CRE Ch. 6 - Prob. 34CRE Ch. 6 - Prob. 35CRE Ch. 6 - Prob. 36CRE Ch. 6 - Prob. 37CRE Ch. 6 - Prob. 38CRE Ch. 6 - Prob. 39CRE Ch. 6 - Prob. 40CRE Ch. 6 - Prob. 41CRE Ch. 6 - Prob. 42CRE Ch. 6 - Prob. 43CRE Ch. 6 - Prob. 44CRE Ch. 6 - Prob. 45CRE Ch. 6 - Prob. 46CRE Ch. 6 - Prob. 47CRE Ch. 6 - Prob. 48CRE Ch. 6 - Prob. 49CRE Ch. 6 - Prob. 50CRE Ch. 6 - Prob. 51CRE Ch. 6 - Prob. 52CRE Ch. 6 - Prob. 53CRE Ch. 6 - Prob. 54CRE

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Find the volume V of solid whose base is the semicircle y = 9 − x 2 , where − 3 ≤ x ≤ 3 .The cross section perpendicular to x -axis is square.

Solution Summary: The author calculates the volume V of a solid whose base is the semicircle y = 9 x 2 and the cross section perpendicular to X -axis is square.

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Find the volume $V$ of solid whose base is the semicircle $y = \sqrt{9 - x^{2}}$ , where $- 3 \leq x \leq 3$ .The cross section perpendicular to $x$ -axis is square.

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Chapter 6 Solutions

Find the volume V of solid whose base is the semicircle y = 9 − x 2 , where − 3 ≤ x ≤ 3 .The cross section perpendicular to x -axis is square.

Solution Summary: The author calculates the volume V of a solid whose base is the semicircle y = 9 x 2 and the cross section perpendicular to X -axis is square.

Videos

Find the volume V of solid whose base is the semicircle y=9−x2, where −3≤x≤3.The cross section perpendicular to x-axis is square.

Want to see the full answer?

Chapter 6 Solutions

Find the volume $V$ of solid whose base is the semicircle $y = \sqrt{9 - x^{2}}$ , where $- 3 \leq x \leq 3$ .The cross section perpendicular to $x$ -axis is square.