1998 AHSME Problem 18
Geometry
Level
2
A right circular cone of volume A, a right circular cylinder of volume M, and a sphere of volume C all have the same radius, and the common height of the cone and the cylinder is equal to the diameter of the sphere. Then:
2A + 2M = 3C
A + M = C
2A = M + C
A - M + C = 0
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1 solution
volume of the cylinder is πr²h and the volume of the cone is πr²h/3, so 3A=M. The volume of the sphere is 4πr³/3, and h=2r, then C=2πr²h/3, C=2A. With A-M+C=0, we can get into A-3A+2A=0 wich is the correct answer.