Calculus II Help

[szskateman22]

So I have this question and I need some help with it:

With some geometric reasoning, one can show that the area of a regular polygon is given by:

A = ([n cot(pi/n)]/4)*l^2, where the n sides all have length l.

A is seen here:

A.) Use an integral to derive a formula for the volume of a "polygonal cone", a cone whose base is a regular polygon, with sides of length l, and height h.

B.) Explain briefly why there is a factor of 1/3 in the volume formulas for cone-like shapes.

• Draw relevant diagram(s) with coordinate axes included.
• Use the coordinates on the diagram(s) to write out equations that describe the relevant shape(s).
• Label/explain all pieces of your integral expression.
• Use a sentence (or two) to describe how your integral "accumulates" the volume.

I am not sure what exactly I'm supposed to be drawing or how to explain it. If anyone could explain how I'm supposed to start this or what would be the best way to explain it, it would be greatly appreciated.

Thanks!