Question

Find the volume of this cone​

Answer 1

Answer:

$\frac{6400\pi}{3}\approx 6702.06\:\mathrm{cm^3}$

Step-by-step explanation:

The volume of a cone is given by $V=\frac{1}{3}\cdot r^2\pi\cdot h$.

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:

$\frac{5}{h_s}=\frac{20}{12+h_s},\\\\20h_s=5(12+h_s),\\\\20h_s=60+5h_s,\\\\15h_s=60,\\\\h_s=4$

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

$V=\frac{1}{3}\cdot 16\cdot 20^2\cdot \pi =\frac{6400\pi}{3}\approx \boxed{6702.06\:\mathrm{cm^3}}$