A rectangular parallelepiped is described around a cylinder whose axis radius is 2, the volume of the parallelepiped

univerkov | August 11, 2021 | education

A rectangular parallelepiped is described around a cylinder whose axis radius is 2, the volume of the parallelepiped is 20, find the surface and the volume of the cylinder.

The radius of the circle at the base of the cylinder is equal to half the length of the side of the base of the parallelepiped described about it.

CD = 2 * R = 2 * OA = 2 * 2 = 4 cm.

The base area of the parallelepiped is: S1 = CD ^ 2 = 16 cm2.

Let us determine its height through the volume of the parallelepiped.

V1 = S1 * AB.

AB = V1 / S1 = 20/16 = 5/4 cm.

The height of the parallelepiped is equal to the height of the cylinder.

Determine the area of the base of the cylinder. Sb = π * ОА ^ 2 = 4 * π cm2.

Let us determine the area of the lateral surface of the cylinder. Side = 2 * π * ОА * AB = π * 2 * 2 * 5/4 = 5 * π cm2.

Then Sпов = 2 * Sсн + S side = 2 * 4 * π + 5 * π = 13 * π cm2.

Determine the volume of the cylinder. V = Sbn * AB = 4 * π * 5/4 = 5 * π cm3.

Answer: The surface area of the cylinder is 13 * π cm2, the volume of the cylinder is 5 * π cm3

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