The height of a right circular cone is trisected by two planes parallel to its base. What is the ratio of the three volumes (top to bottom)?
Show answer & explanation
Correct answer: A
Explanation
The height of the cone is divided into 3 equal parts.
According to the formula: Volumes of similar cones = (Height)³
Upper small cone: (1/3)³ = 1/27
Cone extending to 2/3 of the height (from the top): (2/3)³ = 8/27
Middle section = 8/27 − 1/27 = 7/27
Lower section = 1 − 8/27 = 19/27
Ratio = 1 : 7 : 19