1. Who was the first to give the correct formula for the volume of a
sphere and how was the formula obtained?
2. In his famous derivation of the relation between the volumes of the
sphere, cylinder and the cone, Archimedes uses the formula for volume of
a cone to find the volume of a sphere. My question is how was the volume
of a cone found?
3. If the volume of the cone was found by the `devil's staircase' method
(approximating with thin cylindrical slices of decreasing dia stacked on
top of each other), then the same method could also have been applied to
find the volume of a sphere using the Pythogoras theorem to obtain the
relation for the radius at different heights. (The devil's staircase
method also requires one to know the sum of a sequence of squares of
integers and some idea of what happens in the limit.)
4. It seems to me then that the volume of a sphere could not have been
any more difficult than the volume of a cone.
5. My last question is - which was found first - formula for the volume
of a sphere or for the surface area of a sphere?
__________________________________________________
K. Subramaniam
Homi Bhabha Centre for Science Education
Tata Institute of Fundamental Research
V.N. Purav Marg,
Mankhurd, Mumbai - 400 088
INDIA
e-mail: subra@tifr.res.in