A cone is inscribed in the ball so that the center of the base of the cone coincides with the center of the ball.

| March 18, 2021 | education

A cone is inscribed in the ball so that the center of the base of the cone coincides with the center of the ball. Find the radius of the ball if the length of the generatrix of the cone is 2√3.

Since, by condition, the center of the base of the cone coincides with the center of the circle, the diameter of the base of the cone is equal to the diameter of the ball.

Triangle ABC is isosceles, since AB and BC are apothems of the cone. The height of the cone is equal to the radius of the ball and divides its base AC in half.

Since the angle ABC is based on the diameter of the circle, then its value is 900, therefore, the triangle ABC is isosceles and rectangular, then, according to the Pythagorean theorem:

AC ^ 2 = AB ^ 2 + BC ^ 2 = (2 * √3) ^ 2 + (2 * √3) ^ 2 = 12 + 12 = 24.

AC = √24 = 2 * √6 cm.

Then AO = R = AC / 2 = 2 * √6 / 2 = √6 cm.

Answer: The radius of the ball is √6 cm.



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