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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 ‒ *x*^{2} and the *x*-axis*.* Cross-sections perpendicular to the *y*-axis are quarter-circles.

To determine

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

**Given:**

The base of the solid region is enclosed by *x*-axis.

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

**Calculation:**

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

Consider that the cross-section is a quarter circle with radius

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

The region lies between

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

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

Single Variable Calculus: Early Transcendentals

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