The smaller cone is replaced with another cone of equal radii, but a height twice as big. how many of the new small cone would be needed in order to have the same total volume as the larger cone?

Let's make this simple. Let's have the small cone have a radius 1 and the height 1. This would make the bigger cone have a radius of 1 and the height of 2.

With this information, lets get the volume of both cones. The formula is this:



Plug in numbers:
Small cone:
Big cone:

The small cone has a volume of
The big cone has a volume of

Now, you want to find how many small cones you need to have the same total volume of the big cone.



You have the difference of pi over 3 comparing the big cone to the small one. You realize that the small cone has the same volume of that. Therefore, you need 2 small cones to have the same total volume as the larger cone