Explanation Given: The region is defined by 4 − x 2 − y 2 ≤ z ≤ 10 − 4 x 2 − 4 y 2 Calculation: Consider 4 − x 2 − y 2 ≤ z ≤ 10 − 4 x 2 − 4 y 2 The intersection curve is 4 − x 2 − y 2 = 10 − 4 x 2 − 4 y 2 3 x 2 + 3 y 2 = 6 x 2 + y 2 = 2 The cylindrical coordinates are x = r cos θ , y = r sin θ , z = z Here, 4 − r 2 ≤ z ≤ 10 − 4 r 2 and 0 ≤ r ≤ 2 , 0 ≤ θ ≤ 2 π So, the volume of the given region is ∫ ∫ W ∫ d V = ∫ θ = 0 2 π ∫ r = 0 2 ∫ z = 4 − r 2 10 − 4 r 2 r d z d r d θ

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16, Problem 23CRE

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The volume of the region defined by $4 - x^{2} - y^{2} \leq z \leq 10 - 4 x^{2} - 4 y^{2}$ using cylindrical coordinates.

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Chapter 16, Problem 22CRE

Chapter 16, Problem 24CRE

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Chapter 16 Solutions

CALCULUS (CLOTH)

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The volume of the region defined by 4 − x 2 − y 2 ≤ z ≤ 10 − 4 x 2 − 4 y 2 using cylindrical coordinates.

Solution Summary: The author calculates the volume of the region defined by 4 x 2 y 2 using cylindrical coordinates.

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To calculate:

The volume of the region defined by $4 - x^{2} - y^{2} \leq z \leq 10 - 4 x^{2} - 4 y^{2}$ using cylindrical coordinates.

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Chapter 16 Solutions

The volume of the region defined by 4 − x 2 − y 2 ≤ z ≤ 10 − 4 x 2 − 4 y 2 using cylindrical coordinates.

Solution Summary: The author calculates the volume of the region defined by 4 x 2 y 2 using cylindrical coordinates.

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To calculate: The volume of the region defined by 4−x2−y2≤z≤10−4x2−4y2using cylindrical coordinates.

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Chapter 16 Solutions

To calculate:

The volume of the region defined by $4 - x^{2} - y^{2} \leq z \leq 10 - 4 x^{2} - 4 y^{2}$ using cylindrical coordinates.