# The ball with center O touches the plane at point A. Point B lies in the plane of tangency.

The ball with center O touches the plane at point A. Point B lies in the plane of tangency. Find the volume of the ball if AB = 21cm, BO = 29cm.

Consider a triangle OAB. He has an angle A = 900, since point A is tangent to the plane of the ball, and the segment OA is the radius of the ball, and the radius drawn to the point of tangency forms a perpendicular to the plane, hence the triangle OAB is rectangular. Using the Pythagorean theorem, we find the radius of the ball.

OA ^ 2 = OB ^ 2 – AB ^ 2 = 29 ^ 2 – 21 ^ 2 = 841 – 441 = 400.

ОА = R = 20cm.

Then the volume of the ball is: V = 4 * n * R ^ 3/3 = 4 * n * 8000/3 = 32000 * n / 3 = 10666 (2/3) cm3.

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