The surface area of a sphere

Here's a funny trick. Take an orange, the roundest one you can find, and a pen. Put the orange on a piece of paper. Place the pen next to the orange, like this, and draw a circle on the paper. Draw carefully so that the circle repeats the shape of the orange.

Draw several circles this way. Then peel the orange, and put the pieces together so they fit inside the circles without gaps and overlapping between the pieces. How many circles can you fill with the orange peel? If you do this carefully, and use a completely spherically orange, you can fill exactly four circles, because a ball's surface is exactly four times the area of a circle of the same radius. And since you can calculate the area of a circle as Pi times radius squared, you can calculate the ball's surface as four times Pi times radius squared, simple.

A couple of facts about balls. A ball is a solid body, like a bowling ball or a canon ball. A ball's surface has a name of its own: a sphere. A soap bubble is almost a perfect sphere. Or, think of the planet Earth and its atmosphere.

The planet is solid. The atmosphere is a thin surface. There is a point exactly in the middle of a sphere. A sphere is a surface that consists of all points that are at the same distance from the center point in three dimensions. A sphere is the smallest possible surface that can contain a certain volume.

This means that if you were to make a container that would hold, for example, one liter, and you wanted to make it from as little material as possible, you would have to shape it like a sphere. Any other shape needs a larger surface area to contain one liter. This is why the soap bubble and the planet Earth are round. And, the orange.