Problem

Use cylindrical shells to find the volume of the …

01:15

Problem 46 Hard Difficulty

Use cylindrical shells to find the volume of the solid.

The solid torus of Exercise 6.2.63

Answer

2$\pi^{2} R r^{2}$

Top Calculus 2 / BC Educators

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

Video Transcript

we have been instructed to use cylindrical shells, which means we have something looking like this. We have our capital. Are we ever Laure kissed there? Which means we have to calculate the volume of two pi times capital R times, the radius times of high times d of X. So in this case, we know we're gonna be doing square root of R squared minus X squared detox minus two pi times the integral from negative or are axe Times Square are squared minus X squared D x, which gives us two times capital are times pi times 1/2 pi r squared times to pied time zero which is obviously gonna be zero because when we put in the zero, let me just get zero which is capital are times pi r which is squared, which is our solution because remember, we had a symmetric and travel and the problem, which was why we had a zero value. Because if you look at this, you'll see the circle is where the circles us symmetrical on both sides because, remember were using cylindrical shells for this question. So this expanded out is to pi squared capital are lower case R squared

Amrita B.

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 3

Volumes by Cylindrical Shells

Problem