A regular quadrangular prism is described around a cylinder. the side of the base of this prism is 4

A regular quadrangular prism is described around a cylinder. the side of the base of this prism is 4, and the length of the lateral rib is 503 / p. find the volume of the cylinder

Since the prism is correct, there is a square at its base.

Then the diameter of the circle at the base of the inscribed cylinder is equal to the side of the square ABCD.

Then R = AB / 2 = 4/2 = 2 cm.

Determine the area of the base of the cylinder.

Sp = π * R ^ 2 = π * 4 cm2.

The lateral edge of the quadrangular prism is the height of the cylinder.

Then the volume of the cylinder is:

Vcyl = Scr * AB = π * 4 * 503 / π = 2012 cm3.

Answer: The volume of the cylinder is 2012 cm3.