Question

Where does the formula for a cylinder derive from?

I've been trying to figure it out for an assignment for a while, debating over either a rectangular prism or circle. Which one is it and why?

Answer 1

I am just asking for either an answer of circle or rectangular prism with an explanation.

Answer 2

A cylinder is another type of right prism which has a circle as its base.

Answer 3

I don't know if that answers your question or not, sorry

Answer 4

Are you talking about the volume?

Answer 5

so, immagine 3 space

Answer 6

you have this circle centered at the origin right? what happens if you leave the x and y component the same but mess with the z?

Answer 7

The formula for the volume of a right circular cylinder comes from looking at the formula for the volume of a right prism.

The volume of a right prism is Bh where B is the area of the base and h is the height.
If the prism's base has N sides, then as N increases without bound, the polygon which is the base of the prism has a circle as its limiting form.

Also, the right prism "rounds out" as the number of base edges increases.This is the result of the rectangular lateral sides becoming increasingly smaller in width.

The right prism of infinitely many base edges "becomes" a right circular cylinder.
The B in the V=Bh formula is still B for base but the base is a circle.

Answer 8

@MathematicsNerd

Answer 9

@MathematicsNerd , some commentary from you would be nice