Who calculated the volume of a sphere by comparing it to a cylinder? pythagoras euclid archimedes socrates

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:

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

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have