SOLUTION: A cone frustum is inscribed in a sphere of radius 13. If one of the bases of the frustum is a great circle of the sphere, and the other base has radius 12, what is the slant height

Algebra ->  Bodies-in-space -> SOLUTION: A cone frustum is inscribed in a sphere of radius 13. If one of the bases of the frustum is a great circle of the sphere, and the other base has radius 12, what is the slant height      Log On


   



Question 1137432: A cone frustum is inscribed in a sphere of radius 13. If one of the bases of the frustum is a great circle of the sphere, and the other base has radius 12, what is the slant height.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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1.  The height of the frustum is equal to the distance from the center of the sphere to the smaller base of the frustum


    h = sqrt%2813%5E2-12%5E2%29 = sqrt%2825%29 = 5 units.



2.  Hence, the slant height is equal to


    H = sqrt%28h%5E2+%2B+%28R-r%29%5E2%29 = sqrt%285%5E2+%2B+%2813-12%29%5E2%29 = sqrt%2825+%2B+1%29 = sqrt%2826%29.    ANSWER

Solved.