Question

Who calculated the volume of a sphere by comparing it to a cylinder? Pythagoras Euclid Archimedes Socrates

Answer 1

Answer:

Archimedes

Step-by-step explanation:

The calculation of the volume of the sphere was one of the discoveries that Archimedes most esteemed of all the many he made in his life. He came to demonstrate in a very original way that the volume of the sphere is equal to two thirds of the volume of the circular cylinder circumscribed to it.

Archimedes departed from a semisphere of radius R and placed next to it a straight cone and a straight circular cylinder, both with radius base also R:

Next, he cut the three figures with a plane parallel to the base of the cylinder and studied how the sections that this plane would create in each of the figures would be:

Cylinder: circumference of radius  R.

Semisphere: also a circle but of a different radius.

Cone: Also a circumference.

If for each slice you have the previous relationship it seems quite clear that the volumes follow the same relationship. Hence:

Cylinder volume = Semisphere volume + Cone volume

Archimedes knew the volumes of the cylinder and the cone, so:

$Semisphere\hspace{3}volume=Cone\hspace{3}volume-Cylinder\hspace{3}volume\\Semisphere\hspace{3}volume=\pi R^{3} -\frac{1}{3}\pi R^{3} =\frac{2}{3}\pi R^{3}$

Multiplying by 2 we obtain the volume of a sphere of radius R:

$Sphere\hspace{3}volume=\frac{4}{3}\pi R^{3}$