# A cylinder with a radius r is inscribed in a sphere of radius R. Find the volume of the cylinder.

Let’s draw a segment OB, the length of which is equal to the radius of the sphere. OB = R.

From the right-angled triangle OO1B, by the Pythagorean theorem, we determine the length of the leg OO1.

OO1 ^ 2 = OB ^ 2 – BO1 ^ 2 = R ^ 2 – r ^ 2.

The segment OO1 is half the length of the height of the inscribed cylinder, then AB ^ 2 = 2 * OO1 = 2 * (R ^ 2 – r ^ 2).

AB = √ (2 * (R ^ 2 – r ^ 2)) see.

Determine the area of the base of the cylinder.

Sop = n * r ^ 2.

Determine the volume of the cylinder

V = Sax * AB = n * r ^ 2 * √ (2 * (R ^ 2 – r ^ 2)) cm3.

Answer: The volume of the cylinder is n * r ^ 2 * √ (2 * (R ^ 2 – r ^ 2)) cm3.

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