3.2 Surface Area of Spheres

http://tube.geogebra.org/material/show/id/167797 (Download GeoGebra file)

Drag the red point to see how a sphere can be dissected into n pyramids (approximate) of heights equal the radius r.

Let A1, A2, ..., An be the base areas of the pyramids.

(a) Show that 1/3 (A1+ A2 + ... + An) r ≈ Volume of the sphere

(a) When n tends to infinity, show that

1/3 S r = V

where V and S are the volume and surface area of the sphere respectively.

Hence show that

S = 4 π r² .