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 . |

Key Stage 3 (Junior Secondary) > 3.2 Measures, Shape & Space 度量、圖形與空間 > More about Areas and Volumes >