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R F
R F asked in Science & MathematicsMathematics · 1 month ago

a sphere intersects a plane that is 6 units away from its center; the intersection is a circle of radius 8. what is the radius of the sphere?

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  • Pope
    Lv 7
    1 month ago

    Let K be the center of the sphere.

    Let L be the center of the circle of intersection.

    Let M be any point on the circle of intersection.

    Those three points form a right triangle.

    ∠KLM = 90° ... (by symmetry)

    KL = 6 ... (given)

    LM = 8 ... (given)

    KM = radius of the sphere

    You are familiar with the Pythagorean theorem, right?

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