# Surface Area of Spheres with Proof

- Author:
- Anthony OR 柯志明

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 .