(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 region bounded by the curve y = x and the lines y = 2 and x = 0 . Calculation: Provide the Equation of circle as shown below. y = x Sketch the region in the second quadrant bounded by the curve y = x and the lines y = 2 and x = 0 as shown in Figure 1. Refer to Figure 1. The outer radius R ( x ) = 2 . The inner radius r ( x ) = x . The region lies between 0 to 4. 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 2 for R ( x ) , x for r ( x ) , 0 for a , and 4 for b in Equation (1) (b) To determine Calculate the volume of the solid generated by revolving the region about y axis. (c) To determine Calculate the volume of the solid generated by revolving the region about the line y = 2 . (d) To determine Calculate the volume of the solid generated by revolving the region about the line x = 4 .

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Author: WEIR

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Question

Chapter 6.1, Problem 49E

(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.

(c)

To determine

Calculate the volume of the solid generated by revolving the region about the line y=2.

(d)

To determine

Calculate the volume of the solid generated by revolving the region about the line x=4.

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Chapter 6.1, Problem 48E

Chapter 6.1, Problem 50E

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