1954 AHSME Problems/Problem 27
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Problem 27
A right circular cone has for its base a circle having the same radius as a given sphere. The volume of the cone is one-half that of the sphere. The ratio of the altitude of the cone to the radius of its base is:
Solution
Because the circle has the same radius as the sphere, the cylinder and sphere have the same radius. Then from the volume of cylinder formula, we have