(a) Explanation Given: The region is bounded by the curve y = r x h and the x axis with x = h . Formula used: The volume of the hemisphere (disk method about x axis) is V = ∫ a b π ( f ( x ) 2 − g ( x ) 2 ) d x , where f ( x ) and g ( x ) is mentioned above. Verification: Let f ( x ) = r x h and g ( x ) = 0 . The curves are f ( x ) = r x h and g ( x ) = 0 . Let l = f ( x ) 2 − g ( x ) 2 . To calculate the volume of the hemisphere, first calculate the value of l with f ( x ) = r x h and g ( x ) = 0 as follows, l = ( r x ) 2 − ( 0 ) 2 = r 2 x 2 To find the limit of the integration, it is enough to find the intersection point of the curves f ( x ) = r x h and g ( x ) = 0 (b) To determine To find: The volume of the hemisphere of radius r when the region R is revolving about the x axis using shell method. c. To determine To find: The volume of the hemisphere using general slicing method and keep the base of the hemisphere on the xy plane.

MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134856926

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 6.4, Problem 52E

(a)

To determine

To verify: The volume of the right circular cone of radius r and height h is πr2h3 when the region R revolves about the x axis using disk method.

(b)

To determine

To find: The volume of the hemisphere of radius r when the region R is revolving about the x axis using shell method.

To determine

To find: The volume of the hemisphere using general slicing method and keep the base of the hemisphere on the xy plane.

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Chapter 6.4, Problem 51E

Chapter 6.4, Problem 53E

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MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)

Ch. 6.1 - A police officer leaves his station on a...Ch. 6.1 - Describe a possible motion of an object along a...Ch. 6.1 - Is the position s(t) a number or a function? For...Ch. 6.1 - Without doing further calculations, what are the...Ch. 6.1 - Suppose (unrealistically) in Example 3 that the...Ch. 6.1 - Is the cost of increasing production from 0000...Ch. 6.1 - Explain the meaning of position, displacement, and...Ch. 6.1 - Suppose the velocity of an object moving along a...Ch. 6.1 - Given the velocity function v of an object moving...Ch. 6.1 - Explain how to use definite integrals to find the...

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To verify: The volume of the right circular cone of radius r and height h is π r 2 h 3 when the region R revolves about the x axis using disk method.

Solution Summary: The author explains how the volume of the right circular cone of radius r and height h is bounded by the curve y=rxh and the x axis with

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To verify: The volume of the right circular cone of radius r and height h is πr2h3 when the region R revolves about the x axis using disk method.

To find: The volume of the hemisphere of radius r when the region R is revolving about the x axis using shell method.

To find: The volume of the hemisphere using general slicing method and keep the base of the hemisphere on the xy plane.

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