# Football

In the past, in America, before American football, with its helmets and protectors, became fashionable, European football was played with a rubber ball. We lived in the country and used to ask for the ball by mail. There was a sports shop that had a catalog with the different sizes, and in the order we had to give “the exact number of inches” that we wanted the ball to have. We were asked to give the size in inches, but as we did not know if the inches referred to those of the surface of the rubber ball or the cubic inches of the air contained in the ball, then we asked for a ball that had the same cubic inches of air than of surface.

What was the diameter of the ball we asked for?

#### Solution

The cubic area of ​​the ball can be made of a lot of small pyramids, with their bases representing the surface, and the cusps being in the center of the ball. We know that the volume of a pyramid is equal to its base multiplied by 1/3 of its height.

Therefore, the volume of the sphere is equal to the sum of the bases multiplied by 1/3 of its constant height. That is, the surface of the sphere by 1/3 of its radius. If this volume is equal to the surface, 1/3 of the radius is unit, so if the radius is 3 and The diameter is 6.