Solid with Regular Hexagonal Base: Cross Sections Parallel to yAxis are also Regular Hexagons
This solid has a base that is a regular hexagon.
For this solid, cross sections parallel to the yAxis are also regular hexagons.
1) Question for Both Non-Calculus Students & Calculus Students:
Suppose each side of this regular hexagonal base = 10. Let upper(x) = the upper function (drawn above the xAxis). Let lower(x) = the lower function (drawn below the xAxis). Author piecewise functions for upper(x) and lower(x). Note how 2 vertices of this regular hexagonal base lie on the xAxis itself.
2) Question for Calculus Students:
Write and evaluate definite integral(s) that gives the volume of such a solid described above.