SOLUTION: A cone with a base radius of 8 cm fits inside a sphere of radius 10cm. The apex of the cone is touching the top of the sphere. Find the perpendicular height.

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Question 1126699: A cone with a base radius of 8 cm fits inside a sphere of radius 10cm. The apex of the cone is touching the top of the sphere. Find the perpendicular height.
Answer by ikleyn(52777) About Me  (Show Source):
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There are two basic configurations and two solutions, respectively. 


One configuration is when the base of the cone and its apex are located in the same hemi-sphere.


Then the distance from the center of the sphere to the base of the cone is  


    sqrt%28R%5E2+-+r%5E2%29 = sqrt%2810%5E2+-+8%5E2%29 = sqrt%28100-64%29 = sqrt%2836%29 = 6 cm.


Hence, the height of the cone is  10-6 = 4 cm.



Another configuration is when the base of the cone and its apex are located in different hemi-spheres.


Then the distance from the center of the sphere to the base of the cone is  the same


    sqrt%28R%5E2+-+r%5E2%29 = sqrt%2810%5E2+-+8%5E2%29 = sqrt%28100-64%29 = sqrt%2836%29 = 6 cm.


But the height of the cone in this case is  10+6 = 16 cm.

Solved.