A company ships spherical lamp shades in cubic boxes. The circumference of the lamp shade is \(9\pi \ cm.\) If the box fits the sphere exactly with the sides of the sphere touching the box, what is the volume of the smallest box the company can use for shipping?

A track is made in the shape of a perfect circle. The diameter of the track is 1 mile. How many complete laps will the cars have to make to have driven at least 600 miles?

A cone is placed inside a cylinder in such a way that the cross section shown below results. The radius of the cylinder is 2 cm. The height of the cylinder is 10 cm and the height of the cone is 5 cm. What is the volume of the cylinder that is not filled by the cone?