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For the following regions R, determine which is greater-the volume of the solid generated when R is revolved about the x-axis or about the y-axis. R is bounded by y = x and y = V8x.

For the following regions R, determine which is greater-the volume of the solid generated when R is revolved about the x-axis or about the y-axis. R is bounded by y = x and y = V8x.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
For the following regions R, determine which is greater-the volume of the solid generated when R is revolved about the x-axis or about the y-axis. R is bounded by y = x and y = V8x.
Transcribed Image Text:For the following regions R, determine which is greater-the volume of the solid generated when R is revolved about the x-axis or about the y-axis. R is bounded by y = x and y = V8x.
Expert Solution
Step 1

Calculus homework question answer, step 1, image 1

About x-axis:

Using Washer method:

Internal radius = r = x2

External radius = R = (8x)1/2

 

 

Step 2

The volume of the solid obtained is given by:

Calculus homework question answer, step 2, image 1

About y-axis:

Calculus homework question answer, step 2, image 2

Again using Washer method:

Internal radius = r = y2/8

External radius = R = (y)1/2

The volume of the resulting solid is given by:

Calculus homework question answer, step 2, image 3

Comapring the values we see:

Calculus homework question answer, step 2, image 4

Hence, volume obtained by revolving the region about x-axis is greater than the volume obtained by revolving the region about y-axis

 

 

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