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Math·Geometry and Trigonometry·Area and volume

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Spheres A and B have a point of tangency at point P, where segment MP is a diameter of sphere A, segment NP is a diameter of sphere B, and point P lies on segment MN. The radius of sphere A is 18 times the radius of sphere B, and the volume of sphere B is $972\pi \text{ cubic inches}$. What is the length, in inches, of segment MN?

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