http://tube.geogebra.org/material/show/id/166700 (Download GeoGebra file) The figure shows a hemisphere of radius r and a cylinder of base radius and height r with an inverted cone of the same height and base radius removed. Drag the red point to see the cross-sections of the two solids at a height h. (a) Express x and y in terms of r and h. (b) Are the cross-sections equal in areas? (c) Hence show that the volume of the sphere of radius r is 4/3 π r³. |
Key Stage 3 (Junior Secondary) > 3.2 Measures, Shape & Space 度量、圖形與空間 > More about Areas and Volumes >