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:
[tex]V = \dfrac{(\pi r^2 h)}{3} [/tex]
Plug in numbers:
Small cone: [tex]V = \dfrac{(\pi 1^2 \times 1)}{3} [/tex]
Big cone: [tex]V = \dfrac{(\pi 1^2 \times 2)}{3} [/tex]
The small cone has a volume of [tex] \dfrac{\pi}{3} [/tex]
The big cone has a volume of [tex] \dfrac{2 \pi}{3} [/tex]
Now, you want to find how many small cones you need to have the same total volume of the big cone.
[tex] \dfrac{2\pi}{3} - \dfrac{\pi}{3} = \dfrac{\pi}{3}
[/tex]
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
