Question

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?

Answer 1

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:


`V = ((\pi r^2 h))/(3)`

Plug in numbers:
Small cone:
`V = ((\pi 1^2 * 1))/(3)`
Big cone:
`V = ((\pi 1^2 * 2))/(3)`

The small cone has a volume of
`(\pi)/(3)`
The big cone has a volume of
`(2 \pi)/(3)`

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


`(2\pi)/(3) - (\pi)/(3) = (\pi)/(3)`

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