Find the distance from the center of the ball to the plane of the section if the radius of the ball is 8cm and the radius of the section is equal to √15cm.
Ball with center O and radius R = 8 cm
Section with center О1 and radius r = √ (15) cm
Find: OO1 -?
Let the radius of the section be the segment O1A, then the triangle OO1A is rectangular (the angle O1 is a straight line), where OO1 is the distance from the center of the ball to the plane of the section, O1A is the radius of the section, OA is the radius of the ball. We apply the Pythagorean theorem:
OO1 ^ 2 + O1A ^ 2 = OA ^ 2
OO1 ^ 2 + r ^ 2 = R ^ 2
OO1 ^ 2 + (√ (15)) ^ 2 = 8 ^ 2
OO1 ^ 2 + 15 = 64
OO1 ^ 2 = 49
OO1 = 7 cm
Answer: 7 cm
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