A plane cuts through a 26 cm diameter sphere, but the closest it gets to the center is 5 cm. What is the area of the intersection of the sphere and the plane?

  144π cm² ≈ 452.4 cm²

Step-by-step explanation:

Consider the triangle formed by the segment from the center of the sphere to the center of the disc of intersection, the radius of the disc of intersection, and the radius of the sphere in the plane of those two segments.

This will be a right triangle with one leg 5 cm and hypotenuse 13 cm. The other leg is the radius of the disc of intersection, which is ...

  r = √(13² -5²) = √144 = 12

The area of the disc of intersection is ...

  A = πr² = 144π ≈ 452.4 . . . square centimeters

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step-by-step explanation: