(c) Archimedes was particularly pleased when he determined the ratio of the volumes of a sphere and cylinder. Determine the ratio of the volume of a sphere to the volume of a cylinder having the same radius, and having height the same as the diameter of the sphere:

The volume of the sphere and the volume of the cylinder can be

expressed in terms of their radius.

Correct response:

The given parameters are;

Radius of the sphere = Radius of the cylinder

Height of the cylinder = Diameter of the sphere

Required:

The ratio of the volume of a sphere to the volume of a cylinder.

Solution:

Let r represent the radius of the sphere, we have;

The diameter of the sphere, D = 2·r

Therefore, the height of the cylinder, h = D = 2·r

The volume of the cylinder is; = π·r²·h

Therefore;

Learn more about the volumes of solids here:

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answer: 0.26

i used the calculator on google