A ball of radius r is inscribed in a regular quadrangular prism, find the volume of the prism.

univerkov | June 9, 2021 | education

Since a ball is inscribed in the prism, such a quadrangular prism is a cube.

The distance from the center of the circle to the point of its tangency in the lateral face of the cube is equal to the radius of the circle, then the diameter of the circle is equal to the length of the edge of the cube.

AB = AD = AA1 = D = 2 * R.

Let’s define the volume of the prism.

V = AB * AD * AA1 = (2 * R) ^ 3 = 8 * R ^ 2 cm3.

Answer: The volume of the prism is 8 * R ^ 2 cm3.

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