Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

A hole of radius $ r $ is bored through the cente…

03:19

Question

Answered step-by-step

Problem 69 Hard Difficulty

A hole of radius $ r $ is bored through the middle of a cylinder of radius $ R > r $ at right angles to the axis of the cylinder. Set up, but do not evaluate, an integral for the volume cut out.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Aparna Shakti
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Aparna Shakti

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

02:12

WZ

Wen Zheng

01:11

Amrita Bhasin

04:16

Linda Hand

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Related Topics

Applications of Integration

Discussion

You must be signed in to discuss.
LD

Lencelord D.

August 25, 2021

Aren't the ends of the cylinder-like solid curved?

Top Calculus 2 / BC Educators
Grace He
Anna Marie Vagnozzi

Campbell University

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

Calculus 2 / BC Courses

Lectures

Join Course
Recommended Videos

0:00

A hole of radius $ r $ is …

03:19

A hole of radius $ r $ is …

06:20

Volume of a Segment of a P…

Watch More Solved Questions in Chapter 6

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72

Video Transcript

in this problem. It is given that a whole of radius R is bored through the middle of this cylinder. Mhm Right. Of radius R. That this capital R is greater than our that is smaller at right angles to the axis of the cylinder. Yeah. Set up But do not evaluate an interior for the volume. Great. Mhm. So here we are given with this. We're asked to find We equals to integration R -R two. And what that where you will be instead of. So how we will calculate. Listen, let us see. So the largest gender access lies in the excess excess straight then Vice where plus, That's where it was to ask where that is capital elsewhere. And after that we will find that equals to plus minus or wrote over ar minus Why is square. Now this height will be one developing obviously yes because we are finding from the middle. Right. So that's where the height is. Double of the trade. No, the smallest slender exercise in that access then x squared plus y squared equals two R squared. Smaller square. That will be given by X equals to plus minus or route over small arms square minus y squared. So the land will be one length will be to root R squared minus one is right square And art is small. Right? This is for the smaller cylinder. Right? So that's where small artist taken. Right? So now the volume of the solid cut out is evaluated as value will be this integration Als hide improvement. We have calculated for largest lender is small incident. How can we write this letters? Right. This is us actually. So this is r squared minus y squared, right? And this will be to route over. I spread my this place but say so. This is actually which was asked and this was given. This limit was given. Anti diva was also given. So we only needed to find this value for this. Well, so this is it. I hope you understood the concept. Thanks. We want to.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
142
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Applications of Integration

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Anna Marie Vagnozzi

Campbell University

Caleb Elmore

Baylor University

Samuel Hannah

University of Nottingham

Recommended Videos

0:00

A hole of radius $ r $ is bored through the middle of a cylinder of radius $ R …

03:19

A hole of radius $ r $ is bored through the center of a sphere of radius $ R > …

06:20

Volume of a Segment of a Paraboloid The region bounded by $y=r^{2}-x^{2}, y=0,$…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started