A solid has a circular base of radius 1. It has parallel cross-sections perpendicular to the base which are equilateral triangles. How do you find the volume of the solid?
1 Answer
Feb 5, 2017
Explanation:
Set the origin of the axis at the center of the circle so that the origin is in the center and the parallel cross-sections have the base of the triangles parallel to the
For every
and since it is equilateral its height will be:
The area of the triangle is then:
and the relative volume element:
Integrating over the interval: