Archimedes method for the volume of a sphere
This is one of Archimedes great achievements. Try to find a formula for the volume of a sphere, when the volume for a cone and cylinder is known. First explore relations between slicing areas. Then use the relation between the red, blue and lightblue slices areas to get a general formula.
1) A circle has the area A = πR², pythagoras theoreme is known. 2) Express the slice areas as functions of slicing height y. 3) Find a relation that holds for any y between 0 and R. 4) Apply the relation on the volumes. 5) Calculate the volume V of a sphere when V(cylinder) = hπR² och V(cone) = (1/3)hπR²,