Question

Find the volume of this cone​

Answer 1

`(6400\pi)/(3)\approx 6702.06\:\mathrm{cm^3}`

Explanation:

The volume of a cone is given by
`V=(1)/(3)\cdot r^2\pi\cdot h`.

In this specific cone, the entire height of the cone is not given. However, we do see that it is broken up into two separate cones. Since one cone is inside/part of the other, these cones must be similar. Therefore, we can set up the following proportion to find the height of the smaller cone.

Let
`h_s` be the height of the small cone:

`(5)/(h_s)=(20)/(12+h_s),\\\\20h_s=5(12+h_s),\\\\20h_s=60+5h_s,\\\\15h_s=60,\\\\h_s=4`

Therefore, the height of the largest cone is
`12+4=16`. Now we have all necessary information to find the volume of the cone:

`V=(1)/(3)\cdot 16\cdot 20^2\cdot \pi =(6400\pi)/(3)\approx \boxed{6702.06\:\mathrm{cm^3}}`