Question 1126699
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There are two basic configurations and two solutions, respectively.



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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(R^2 - r^2)}}} = {{{sqrt(10^2 - 8^2)}}} = {{{sqrt(100-64)}}} = {{{sqrt(36)}}} = 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(R^2 - r^2)}}} = {{{sqrt(10^2 - 8^2)}}} = {{{sqrt(100-64)}}} = {{{sqrt(36)}}} = 6 cm.


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