Explanation Given: Region is bounded below by the plane z =1 and above by sphere x 2 + y 2 + z 2 = 4 Formula used: Volume of a solid using spherical co-ordinates is V = ∭ ρ 2 sin ϕ d ρ d ϕ d θ Calculation: z = 1 ⇒ r cos ϕ = 1 ⇒ cos ϕ = 1 2 ( A s r = 2 ) V o l u m e = ∫ 0 2 π ∫ 0 π 3 ∫ 1 cos ϕ 2 ρ 2 sin ϕ d ρ d ϕ d θ = ∫ 0 2 π ∫ 0 π 3 ( 1 3 ρ 3 ) 1 cos ϕ 2 sin ϕ d ϕ d θ = ∫ 0 2 π ∫ 0 π 3 1 3 ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.4, Problem 43E

To determine

The volume of the region bounded below by the plane z = 1and above by the sphere $x^{2} + y^{2} + z^{2} = 4$ , using spherical co-ordinates.

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Chapter 16.4, Problem 42E

Chapter 16.4, Problem 44E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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The volume of the region bounded below by the plane z = 1and above by the sphere x 2 + y 2 + z 2 = 4 , using spherical co-ordinates.

Solution Summary: The author calculates the volume of a solid using spherical co-ordinates.

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The volume of the region bounded below by the plane z = 1and above by the sphere $x^{2} + y^{2} + z^{2} = 4$ , using spherical co-ordinates.

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Chapter 16 Solutions

The volume of the region bounded below by the plane z = 1and above by the sphere x 2 + y 2 + z 2 = 4 , using spherical co-ordinates.

Solution Summary: The author calculates the volume of a solid using spherical co-ordinates.

Videos

The volume of the region bounded below by the plane z = 1and above by the sphere x2+y2+z2=4, using spherical co-ordinates.

Want to see the full answer?

Chapter 16 Solutions

The volume of the region bounded below by the plane z = 1and above by the sphere $x^{2} + y^{2} + z^{2} = 4$ , using spherical co-ordinates.