Explanation Given: Calculation: Let r be the radius at height y , then by Pythagoras theorem, we get; ⇒ R 2 = ( R − y ) 2 + r 2 ⇒ r 2 = R 2 − ( R − y ) 2 = R 2 − R 2 + 2 R y − y 2 ⇒ r 2 = 2 R y − y 2 Radius, r changes as y changes, so the volume of the filled portion of the sphere is; ⇒ ∫ 0 h π r 2 d y = ∫ 0 h

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6.2, Problem 5E

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Find the volume $V$ of liquid needed to fill a sphere of radius $R$ to height $h$ .

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Chapter 6.2, Problem 4E

Chapter 6.2, Problem 6E

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Let the region R be the area enclosed by the function f(x)= = 3x² and g(x) = 4x. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is an isosceles right triangle with a leg in the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth. y 11 10 9 00 8 7 9 5 4 3 2 1 -1 -1 x 1 2

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Chapter 6 Solutions

CALCULUS (CLOTH)

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

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Find the volume V of liquid needed to fill a sphere of radius R to height h .

Solution Summary: The author explains how the volume V of liquid needed to fill a sphere of radius R to height h is.

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Find the volume $V$ of liquid needed to fill a sphere of radius $R$ to height $h$ .

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Chapter 6 Solutions

Find the volume V of liquid needed to fill a sphere of radius R to height h .

Solution Summary: The author explains how the volume V of liquid needed to fill a sphere of radius R to height h is.

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Find the volume V of liquid needed to fill a sphere of radius R to height h.

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Chapter 6 Solutions

Find the volume $V$ of liquid needed to fill a sphere of radius $R$ to height $h$ .