Problem

Find the volume of the described solid $ S $. Th…

01:10

Problem 56 Hard Difficulty

Find the volume of the described solid $ S $.
The base of $ S $ is the triangular region with vertices $ (0, 0) $, $ (1, 0) $, and $ (0, 1) $. Cross-sections perpendicular to the y-axis are equilateral triangles.

Answer

$\frac{\sqrt{3}}{12}$

More Answers

01:59

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

Anna Marie V.

Campbell University

Kristen K.

University of Michigan - Ann Arbor

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

Uniqlo. Emerald Triangle has three angles that are each 60 degrees because it adds upto 1 80 degrees 1 80 Divide by 360 degrees. Therefore, we know our h is sign of 60 degrees squirt of three over two times us. Which means of R A is 1/2 ass times h. Let's plug in what we know. So this is our age we're putting in right over here again. I said 1/2 s times h. Remember, the line representing the diagonal is X equals negative y plus one specified in the problem knowing that we can integrate from 0 to 1. We have squirt of three over four a square deal. Y Okay, Squirt, if there were four is a constant. Which means we're gonna be plugging this out. Pull it out on the outside of the integral from 01 We just established that we can plug end What s is negative. Why plus one squared. We established that in the previous slide, which means now we can integrate. We can do this by using the power rule. Increase the exponent by one divide by the new exponents because you can see I end up with wondered Why Cubed mice westward Plus why? Okay, now we have this next step is to plug in the bounds here. So in other words, plug in the values on the outside of the integral and we end up with squirt of three over 12 is our solution.

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

Anna Marie V.

Campbell University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Joseph L.

Boston College