Jeff conducts an experiment. He pours 5 cm of water into a cylindrical container with a base diameter of 12 cm. He places a ball of radius R in the container and notices that the water covers it perfectly (the surface of the water is therefore tangent to the ball at the bottom of the container).

- volume of a cylinder : [tex]\pi r^2h[/tex]
- volume of a ball : [tex]\frac{4}{3} \pi r^3[/tex]

Show that the volume of water can be written as [tex]\pi (72R-\frac{4}{3}R^2 )[/tex]

Thank you for all answers in advance!