Answered: Use the method of cylindrical shells to…

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 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...

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I am having a problem finding the correct answer to this problem. I have tried interpreting for y using the cylindrical method and got 2pie as well as 16pie/15 as an answer which both were wrong. I don't know what I'm doing wrong.

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis.
x = 4y2, y > 0, x = 4; about y = 2

Expert Solution

Step 1:Introduction

Volume by cylindrical shells $v = \int_{a}^{b} 2 πxf (x) d x$

where, x = radius of the cylinder, f(x) = height of the cylinder

dx = thickness of the cylinder shells

a,b limits of the height

given the region bounded by the curves.

$x = 4 y^{2}, y ⩾ 0, x = 4; a b o u t y = 2$

since the rotation of the curve is around the x-axis(parallel to). The volume will be horizontal in nature.

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