Answer: Choice A
The formula for the volume of a cone is 1/3 the volume of a cylinder. The volume of a sphere is 4/3 the volume of a cylinder, where the height of the cylinder is the same as the radius of the sphere
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Explanation:
As the first screenshot shows, the volume of a cone is 1/3 the volume of a sphere. The radius of each are the same. The height of each are the same as well.
The first screenshot also mentions "The volume of the half sphere is 2/3 the volume of the cylinder". The diagram shows the height of the cylinder (h) is equal to the radius of the half sphere. Based on this, the volume of a full sphere of radius r will be 4/3 times the volume of the cylinder with the same radius and height of 2r. You can think of having a spherical tennis ball inside a cylindrical can.
The first screenshot shows this when your teacher computed [tex]2*\frac{2}{3}*\pi*r^2*r[/tex] to get [tex]\frac{4}{3}\pi*r^3[/tex]
Note how [tex]\frac{4}{3}\pi*r^3 = \frac{4}{3}\left(\pi*r^2*r\right)[/tex]
The stuff in parenthesis represents the volume of a cylinder with radius r and height h = r. This is one way to see that
SphereVolume = (4/3)*(CylinderVolume)
where the height of the cylinder is as discussed above.
