Answer:
The height of the cone is 18 cm
The height of the hemisphere is 6 cm
The exact volume of the cone is 216 pi cm^3
The exact volume of the hemisphere is 144 pi cm ^3
Step-by-step explanation:
Since the height of the entire figure is 24 then the height of the cone is 18 cm. This is true since a hemisphere is half a sphere and its height will be its radius which is 6. The height if the hemisphere is 6. So 24 - 6 = 18, the height of the cone.
The volume of the cone is found using the volume formula for a cone [tex]V=\frac{1}{3}\pi r^2h[/tex].
Substitute h=18 and r = 6.
[tex]V = \frac{1}{3}\pi r^2h\\V = \frac{1}{3}\pi (6^2)(18)\\V=\frac{1}{3}\pi *36*18\\V = \frac{648}{3}\pi \\V= 216\pi [/tex]
The volume of a hemisphere is half of [tex]V=\frac{4}{3}\pi r^3[/tex]. Substitute r=6.
[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi 6^3\\V=\frac{4}{3}\pi *216\\V=\frac{4*216}{3}\pi\\ V=288\pi[/tex]
However the hemisphere is half this so it is [tex]144\pi[/tex].
