Explanation Given: The cone φ = φ 0 and the sphere ρ = R Formula Used: ∭ W f ( x , y , z ) d V = ∫ δ γ ∫ α β ∫ a b ρ 2 sin φ f ( ρ sin φ cos θ , ρ sin φ s i n θ , ρ cos φ ) d ρ d θ d φ Where a ≤ ρ ≤ b α ≤ θ ≤ β δ ≤ φ ≤ γ Calculation: The given region is: W : 0 ≤ θ ≤ 2 π , 0 ≤ φ ≤ φ 0 , 0 ≤ ρ ≤ R Now, the volume of the region is: ∭ W d V = ∫ 0 2 π ∫ 0 φ 0 ∫ 0 R ρ 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 16.4, Problem 52E

To determine

The volume of the region lying above the cone $φ = φ_{0}$ and below the sphere $ρ = R$ .

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Chapter 16.4, Problem 51E

Chapter 16.4, Problem 53E

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Chapter 16 Solutions

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The volume of the region lying above the cone φ = φ 0 and below the sphere ρ = R .

Solution Summary: The author explains how to determine the volume of the region lying above the cone and below the sphere.

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The volume of the region lying above the cone $φ = φ_{0}$ and below the sphere $ρ = R$ .

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Chapter 16 Solutions

The volume of the region lying above the cone φ = φ 0 and below the sphere ρ = R .

Solution Summary: The author explains how to determine the volume of the region lying above the cone and below the sphere.

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The volume of the region lying above the cone φ=φ0and below the sphere ρ=R.

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Chapter 16 Solutions

The volume of the region lying above the cone $φ = φ_{0}$ and below the sphere $ρ = R$ .