(a) To determine Calculate the volume of the solid generated by revolving the region about x axis. Explanation Given information: The solid generated by revolving the triangular region with vertices ( 0 , 0 ) , ( b , 0 ) , and ( 0 , h ) . Calculation: Sketch the triangular region with vertices ( 0 , 0 ) , ( b , 0 ) , and ( 0 , h ) as shown in Figure 1. Refer to Figure 1. Provide the equation of line as shown below. y = − h b x + h The outer radius R ( x ) = − h b x + h . The inner radius r ( x ) = 0 . The region lies between 0 to b. Calculate the volume of the solid about x axis using the formula: V = ∫ a b π ( [ R ( x ) ] 2 − [ r ( x ) ] 2 ) d x (1) Substitute − h b x + h for R ( x ) , 0 for r ( x ) , 0 for a , and b for b in Equation (1) (b) To determine Calculate the volume of the solid generated by revolving the region about y axis.

Thomas' Calculus - MyMathLab Integrated Review

14th Edition

ISBN: 9780134786223

Author: Hass

Publisher: PEARSON

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Question

Chapter 6.1, Problem 52E

(a)

To determine

Calculate the volume of the solid generated by revolving the region about x axis.

(b)

To determine

Calculate the volume of the solid generated by revolving the region about y axis.

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Chapter 6.1, Problem 51E

Chapter 6.1, Problem 53E

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