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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305270336
Chapter 6.2, Problem 60E
Textbook Problem
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Find the volume of the described solid S.

The base of S is the region enclosed by y = 2 ‒ x2 and the x-axis. Cross-sections perpendicular to the y-axis are quarter-circles.

Chapter 6.2, Problem 60E, Find the volume of the described solid S. The base of S is the region enclosed by y = 2  x2 and the

To determine

To calculate: The volume of the described solid (parabola).

Explanation of Solution

Given:

The base of the solid region is enclosed by y=2x2 and the x-axis.

The cross-sections perpendicular to the y-axis are quarter-circles.

Calculation:

Find the base length of the quarter circle (2x).

x2=2yx=±2y2x=22y

Consider that the cross-section is a quarter circle with radius r=22y.

The cross-section of the solid region as shown in Figure 1.

The region lies between a=0 and b=2.

The expression to find the volume of the solid region as shown below.

V=abA(y)dy (1)

Find the area of quarter circle using the relation as shown below

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Chapter 6 Solutions

Single Variable Calculus: Early Transcendentals
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