Multiple Choice Question (MCQ)

To identical spheres of radius 6 intersect so that the distance between their centers is 10. The points of intersection of the two spheres form a circle. What is the area of this circle?

  1. ×

    5\pi

  2. ×

    6\pi

  3. ×

    8\pi

  4. ×

    10\pi

  5. 11\pi

Collected in the board: Solid Geometry

Steven Zheng posted 2 months ago


Answer

  1. Plot the sketch of the cross section of the two spheres intersecting each other. Drop an altitude from one of the intersecting point to the segment connecting the two centers.


    The altitude is the radius of the circle formed by the points of intersection of the two spheres. The measure of the radius is,


    r = \sqrt{6^2-5^2} =\sqrt{11}

    The area of the circle is,

    \pi r^2 = 11\pi

Steven Zheng posted 2 months ago

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