Explanation Given : The region bounded below by the plane z = 1 and above by the sphere x 2 + y 2 + z 2 = 4 Calculation : Step 1: Rewrite x 2 + y 2 + z 2 = 4 as z 2 = 4 − x 2 − y 2 z = ± 4 − x 2 − y 2 Step 2: Now the region bounded below by the plane z = 1 and above by the sphere x 2 + y 2 + z 2 = 4 Z = 1 to 4 − x 2 − y 2 For z = 1, x 2 + y 2 + 1 2 = 4 x 2 + y 2 = 3 Step 3: Now convert to cylindrical coordinates x = r cos θ , y = r sin θ , z=z, d V = r d z d r d θ z → 1 t o 4 − r 2 r → 0 t o 3 θ → 0 t o 2 π Step 4: The volume of the region is defined as: V = ∫ 0 2 π ∫ 0 3 ∫ 1 4 − r 2 r d z d r d θ = ∫ 0 2 π ∫ 0 3 r [ z �...

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.4, Problem 42E

To determine

To calculate: The volume of the region bounded below by the plane z = 1 and above by the sphere $x^{2} + y^{2} + z^{2} = 4$ using the cylindrical coordinates.

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Chapter 16.4, Problem 41E

Chapter 16.4, Problem 43E

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Chapter 16 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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The volume of the region bounded below by the plane z = 1 and above by the sphere x 2 + y 2 + z 2 = 4 using the cylindrical coordinates.

Solution Summary: The author calculates the volume of the region bounded below by the plane z = 1 and above using the cylindrical coordinates.

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To calculate: The volume of the region bounded below by the plane z = 1 and above by the sphere $x^{2} + y^{2} + z^{2} = 4$ using the cylindrical coordinates.

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Chapter 16 Solutions

The volume of the region bounded below by the plane z = 1 and above by the sphere x 2 + y 2 + z 2 = 4 using the cylindrical coordinates.

Solution Summary: The author calculates the volume of the region bounded below by the plane z = 1 and above using the cylindrical coordinates.

Videos

To calculate: The volume of the region bounded below by the plane z = 1 and above by the sphere x2+y2+z2=4 using the cylindrical coordinates.

Want to see the full answer?

Chapter 16 Solutions

To calculate: The volume of the region bounded below by the plane z = 1 and above by the sphere $x^{2} + y^{2} + z^{2} = 4$ using the cylindrical coordinates.