15. Find the volume of the solid obtained by rotating the region bounded by y= - Xx= 2, and y = 0 about the y-axis. Sketch the graph of the region and the solid

Answered: 5. Find the volume of the solid…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...

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1
5. Find the volume of the solid obtained by rotating the region bounded by y
= - X
x= 2, and y = 0 about the y-
axis. Sketch the graph of the region and the solid

Expert Solution

Step 1

In this question we have to find the volume of the region bounded by $y = \frac{1}{4} x^{2}$ , $x = 2$ and $y = 0$ about $y$ -axis.

The formula for the volume by revolution about $y$ -axis in the interval $[a, b]$ is $V = \int_{a}^{b} π [{(f (x))}^{2} - {(g (x))}^{2}] d x$ where, $f (x)$ is the upper curve and $g (x)$ is the lower curve.

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Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed when the region bounded in Quadrant I by the axes and the lines x = 9 and y = 5 is revolved about the a) x-axis b) y-axis

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5. Find the volume of the solid obtained by rotating the region bounded by y =x² , x= 2, and y = 0 about the y- 4 axis. Sketch the graph of the region and the solid