The height of the cone is √3 cm, the generatrix is 2 cm. Find the radius of the described sphere.

The height of the cone, its radius and generatrix form a right-angled triangle AOC, in which, according to the Pythagorean theorem, we determine the length of the leg AO, which is the radius of the circle at the base of the cone.

AO ^ 2 = AC ^ 2 – OC ^ 2 = 4 – 3 = 1 cm.

AO = R = 1 cm.

AB = D = 2 * R = 2 cm.

The axial section of the cone is an isosceles triangle ABC around which a circle is described.

Determine the area of ​​the triangle ABC.

Savs = AB * OC / 2 = 2 * √3 / 2 = √3 cm2.

Determine the radius of the circumscribed circle around the triangle ABC.

R = a * b * c / 4 * Sавс, where a, b, c are the lengths of the sides of the triangle.

R = 2 * 2 * 2/4 * √3 = 2 / √3 = 2 * √3 / 3 cm.

The radius of the ball circumscribed around the cone is equal to the radius of the circle circumscribed around the triangle ABC.

Answer: The radius of the described ball is 2 * √3 / 3 cm.