is the area bounded by: .
Suppose a solid has a base A and the cross-sections of the solid
perpendicular to the y-axis are equilateral triangles.
Sketch solid and find volume.
The base looks like this:Code:| 1| *--------+--------* | x | x * - - - + - - - * * | * * | * - - - - - * - - - - - - |
The area of an equilateral triangle with side is: .
The side of our equilateral triangle is: .
Hence, the area of the triangle is: .
Since , we have: .
Therefore, the volume is: .