🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning Numerade Educator ### Problem 40 Easy Difficulty # Find the volume of the described solid$S .$The base of$S$is the triangular region with vertices$(0,0),$$(1,0), and (0,1) . Cross-sections perpendicular to the y -axisare equilateral triangles. ### Answer ##$$\frac{\sqrt{3}}{12}

#### Topics

Applications of Integration

### Discussion

You must be signed in to discuss.
##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp

### Video Transcript

{'transcript': "to find the volume by slicing cross sections that are prepping nuclear to our X. Access. We have a volume fee. The the volume fee to be equal Sudan's Igra E Why D Why? So the coordinates so too were taken with white access. And we are saying that the coordinates why coordinates why has length Eggs to be equal to 1 -1 way? So the corresponding equilateral triangle has sides. S so the collateral triangle. This triangle has say is we've said is so we've side new side is has the area as area anyway to be called to S square cute Square roots of three divided by four. And this is equal to one minutes wide squared. Yeah then we have Square roots of three divided by four. So this implies that volume V is going to be the integral from 0 to 1 of a. Why the UAE. Which is this folio. So this then it's equal to then see girl 0 to 1. A Y. 81 minus Y squared. You have Square root of three divided by four divided by four. The way. So evaluates defensive girl. If I valid I have these two vehicles. Your constant house so scary over three divided by four out unC grassroots to one. If you expand what you have in the brackets, This gives us 1 -2. Y. Bless Y squared the Y. And this will be square roots of three divided by four. Thank you. Girl of this is white. My next wife squared plus Y cubed divided by three. The N +70 to 1. And this it's equal to Square roots of three divided by swarms. So they volume. It's Square root of three divided by swope us our final So"}

Kwame Nkrumah University of Science and Technology

#### Topics

Applications of Integration

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp