Cavalieri's principle states that if two solids of equal height
have equal cross-sectional areas at every level parallel to
the respective bases, then the two solids have equal
volume.
Therefore, the formula for the volume of the sphere can
derived by writing an expression that represents the
volume of
The two shaded solids both have a height of 2r units. At
every level, the areas of the cross sections of both solids
equal (r? - b?).
one cone within the cylinder
the two cones within the cylinder,
the solid between the two cones and the cylinder,
the cylinder
X
Cross section area -
-
-
(2-0)
Cross section area -
-
)