how to derive surface area of a sphere

We were going to estimate the surface area of a sphere.

1. find the circumference of your orange with the ribbon. Be accurate.
2. using this measurement and prior knowledge, find the radius of the sphere.
3. with the compass draw 6 or so circles with that radius.
4. peel the orange and fill as many circles completely as you can.(only the "orange" part is the surface area)
It was great, we fit exactly 4 circles, (which are of area pi*radius*radius), so we had an estimate of the surface area.