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

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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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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6. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.5.001. ASK YOUR TEACHER PRACTICE ANOTHER Let I = 4 f(x) dx, where f is the function whose graph is shown. = √ ² F(x 12 4 y f 1 2 (a) Use the graph to find L2, R2 and M2. 42 = R₂ = M₂ = 1 x 3 4

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Find a parameterization for a circle of radius 4 with center (-4,-6,-3) in a plane parallel to the yz plane. Write your parameterization so the y component includes a positive cosine.

Chapter 6 Solutions

Calculus - Standalone book

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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 $h$ .