Shown in Fig. 1 is a pile of cylinders that approximates one half of a sphere.
From Fig. 1, we see .
If denotes the volume of cylinder in the pile, then
Similarly, we approximate a cone
by a stack of cylinders:
If denotes the cylinder, then
Since as , , we have
We now derive the formula for a sphere’s surface area.
Let us approximate a sphere by many cones:
From Fig. 3, we see that as ,
It follows that