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imc

geometry intermediate

Problem

A right circular cylinder with its diameter equal to its height is inscribed in a right circular cone. The cone has diameter and altitude , and the axes of the cylinder and cone coincide. Find the radius of the cylinder.
(A)
(B)
(C)
(D)
Solution
Let the diameter of the cylinder be . Examining the cross section of the cone and cylinder, we find two similar triangles. Hence, which we solve to find . Our answer is .
Final answer
B