The radius of the ball is 5 cm. A regular quadrangular prism 8 cm high is inscribed in the ball. Find the volume of the prism.

univerkov | July 19, 2021 | education

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

The diagonal AC1 of the prism is equal to two radii of the circle into which the prism is inscribed. AC1 = 2 * OC1 = 2 * 5 = 10 cm.

Let us define the diagonal of the base of the prism by the Pythagorean theorem.

AC ^ 2 = AC1 ^ 2 – CC1 ^ 2 = 100 – 64 = 36.

AC = 6 cm.

Since there is a square at the base of the prism, AB = AD = BC = DC. Then AB ^ 2 + AC ^ 2 = 2 * AB ^ 2 = AC ^ 2 = 36.

AB ^ 2 = 36/2 = 18.

AB = BC = AD = CD = 3 * √2 cm.

Let’s define the volume of the prism.

V = AB * BC * CC1 = 3 * √2 * 3 * √2 * 8 = 144 cm3.

Answer: The volume of the prism is 144 cm3.

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