Lesson 6ª

THE SPHERE.

We can calculate the surface of a sphere by using half a sphere from a rough material and a very long thread. Fix one end of the thread at the centre of the max. circle of the semi-sphere and begin forming a spiral until you cover its entire surface (see the image below). Notice the amount of thread you need to cover it completely but don't cut the thread:

Now, with the same thread, cover the sphere on the outside:

Check the amount of thread you are missing this second time. If you have done this correctly (in both cases), you will notice that on this second exercise, you are missing twice the amount of thread used on the first exercise.
This means that the surface of the semi-sphere is twice the surface of the max. circle of the sphere. In other words:

If the area of the semi-sphere is , the area of the entire sphere will be:

We can also get the spherical surface using a semi-circumference spinning around its diameter:

A complete turn of the semi-circumference, in other words 360º, generates a spherical surface equal to

15(4).16   Calculate the spherical surface of a ball with a radius of 12 cm.