Answer:
[tex]\frac{6400\pi}{3}\approx 6702.06\:\mathrm{cm^3}[/tex]
Step-by-step explanation:
The volume of a cone is given by [tex]V=\frac{1}{3}\cdot r^2\pi\cdot h[/tex].
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 [tex]h_s[/tex] be the height of the small cone:
[tex]\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[/tex]
Therefore, the height of the largest cone is [tex]12+4=16[/tex]. Now we have all necessary information to find the volume of the cone:
[tex]V=\frac{1}{3}\cdot 16\cdot 20^2\cdot \pi =\frac{6400\pi}{3}\approx \boxed{6702.06\:\mathrm{cm^3}}[/tex]
