Volume of Triangular Solid: A Solution Attempt

[gillyr2]

The attempt at a solution[/b]Question: Find the volume of the solid whose base is the triangular region of the xy-plane with vertices (0,0),(1,0),(0,1) and whose cross sections perpendicular to the y-axis are equilateral triangles.

I have the problem set up. just don't know how to get the cross sections of the triangles. i know the area is 1/2 bh i thought maybe similar triangles where the height would be sqrt(3)/4x and x=1-y. am i close? help

 

[Dick]

Sure, you're close. The base is x=(1-y). The height is base*sqrt(3)/2. So what's the area?

 

[gillyr2]

so the area is sqrt(3)/2 (1-y)^2? and i would just integrate that from 0 to 1 right?

 

[Dick]

Almost right. The area is (1/2)*b*h. What happened to the (1/2)?

 

[gillyr2]

ah. so its sqrt(3)/4 (1-y)^2

 

[Dick]

Yes it is.