Volume by slicing

Volume by slicing

Sec 6.3 Volume by slicing, Q10, pg 430 

Note: Section number refers to Calculus, Early Transcendentals (2nd edition) by Briggs, Cochran, and Gillett.

For this solid, it is possible to find the volume by integration of the cross sectional area. The solid has a circular base of radius r. The cross sections perpendicular to the base and parallel to the z-axis are equilateral triangles.  

The solid

Circular base

A sliced version so that it is possible to see the equilateral triangles:

 

Four slice version by Evelyn Sander.

The 20 slice version Volume: 20 equilateral triangles on circular base, dennedesigns, Jun 29, 2015.