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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.

$$

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

$$

Applications of Integration

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{'transcript': "the problem is finding the volume after described the solid US base of us is a triangular ridden with quantities Sierra zero one zero and Carolan cross sections perpendicular to that. Why access? I think with a little triangles. So first at the note area of the cross section of and eclipse waxes is a why you know why is that this tense? Between this cross section on DH X axis Here at the note side of cross section, it is I. And we have a over one is for you one minus y over one. So a is equal to one minus y. Then the area of the cross section B Y. You see, he caught you. Let's have three over four. Hey, Squires is cultural bit of three ofthe war one minus y squared. So the volume was a sally. The eyes is you can't you into girl from zero to one. A wine. Why, that's the culture into girl From zero to one. Your three or my four one minus y squire. You want the answer? Is you three over twelve"}