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Find the volume of this cone​

Find the volume of this cone​-example-1
User RiaanDP
by
6.4k points

1 Answer

5 votes

Answer:


(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}}

User Mike Seghers
by
6.5k points
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