Answer:
one cone within the cylinder.
Step-by-step explanation:
First of all we have to start with half of a sphere (also known as a hemisphere), whose radius is r, and calculate its volume. Then we can double our answer at the end to find the volume of the complete sphere. But first to apply the Cavalieri's Principle, we start with a cone with the same radius r and suppose the height is also r, so the volume of this cone is:
[tex]V_{cone}=\frac{1}{3}\pi r^{3}[/tex]
Next, let's look at a cylinder and suppose this cylinder also has a radius r and height r, so the volume of this cylinder is:
[tex]V_{cylinder}=\pi r^{3}[/tex]
Next, we place the the cone inside the cylinder and the volume that's inside the cylinder, but outside the cone is:
[tex]V_{cylinder}-V_{cone}=\pi r^{3}-\frac{1}{3}\pi r^{3}=\frac{2}{3}\pi r^{3}[/tex]
And this is the volume of a hemisphere. Finally, if we double this value we get the volume of a complete sphere, which is:
[tex]V_{sphere}=\frac{4}{3}\pi r^{3}[/tex]
