Problem

Find the volume common to two spheres, each with …

View

Problem 66 Hard Difficulty

Find the volume common to two circular cylinders, each with radius $ r $, if the axes of the cylinders intersect at right angles.

Answer

$\frac{16 r^{3}}{3}$

More Answers

04:23

Wen Z.

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Heather Z.

Oregon State University

Michael J.

Idaho State University

Joseph L.

Boston College

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

okay. Recall the fact that we know that Z is a prevalent to the squirt of r squared minus Z squared. Now remember, we know the whole cross section is gonna be four times that. Remember when we square something, it cancels out the square root and the squared sine so we end up with simply four times r squared minus c squared. Now that we have this, we know we can integrate from zero to our And remember, we can actually just double this. This makes it a lot easier because now, instead of having negative bounds who are simply doubling the result, pull out all of our constants. Other words, if we plot before we end up with 82 times four is eight. Integrate. When we integrate, we use the power method, which means we increased the expert by one, we divide by the new expert. Z squared becomes 1/3 c cubed. Now we're at the point where we can plug in our bounds. Remember, we're playing and are on the top and they're playing in zero on the bottom. We plug in zero. We actually just end up with zero minus zero, which is always just zero, which means we have eight times to r cubed over three, which means we end up with 16 r cubed divided by three.

Amrita B.

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Top Calculus 2 / BC Educators

Catherine R.

Missouri State University

Heather Z.

Oregon State University

Michael J.

Idaho State University

Joseph L.

Boston College