Volume of a Cone by Integration

I couldn't find a website for this. I would be happy to talk you through if you would like.

Can I assume you are in Calculus I in college?

An integration allows you to do a sum of infintessimal slices of a function. The key here is *sum*.

First you need to find the function to integrate where the sum of the values will give you the volume. Do you have an idea of what function you can use?

Enthusiast, your question is exactly what I'm after, the summation of little circles as the radius goes to zero (x^2 +y^2=r). Or could it be a voume of revolution about the Y axis where x=y. I need the formulation of the problem.

Either a summation of little circles or a volume of revolution will work (i.e. give the same answer). To me, the little circles is easier.

What value (or property) of the little circles do you think you should sum?

The steps you will then take are as follows.

1. Come up with a function for the value you will sum. This function will contain the constants you listed -- pi, radius at the base and height.

This function will need an additional independent variable that we will integrate over. This will either be the y-value (if you want to do little circles) or an angle measure (for volume of revolution.)

2. Once you have this function you can integrate over the independent variable from step 1.

3. Then you can solve the result as a definite integral and simplify.

If you start with step one. I will help you if you get stuck.

ebrown_p