# A sphere is inscribed in a regular quadrangular prism, find the ratio of the total

August 19, 2021 | education

| **A sphere is inscribed in a regular quadrangular prism, find the ratio of the total surface area of the prism to the total surface area of the sphere.**

Since the sphere is inscribed in the correct prism, this prism is a cube.

Let the length of the cube be equal to X cm, then the area of its lateral faces is equal to X ^ 2 cm2.

Since the cube has six faces, then Sпов = 6 * X ^ 2.

The diameter of a sphere inscribed in a cube is equal to the length of an edge of the cube. D = X cm.

Then the area of the sphere is equal to: Sсф = π * D ^ 2 = π * X ^ 2.

Let’s define the area ratio.

Sпов / Sсф = 6 * X ^ 2 / π * X ^ 2 = 6 / π.

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