A solid right circular cone is cut perpendicular to its height from base in ratio 2:3 Find the ratio of volume of upper half to lower half. एक ठोस लम्बवृत्तीय शंकु को ऊंचाई के लम्बवत आधार से 2: 3 के अनुपात में काटा जाता है ऊपरी आधे हिस्से तथा निचले आधे हिस्से के आयतन का अनुपात ज्ञात करें ।

When a cone is cut parallel to its base, the upper portion is a smaller similar cone. The height ratio is 2:3 from base, meaning the upper cone has height 3/5 of the original. For similar cones, volumes are proportional to the cube of the height ratio. Upper cone volume = (3/5)^3 = 27/125 of the original. Lower frustum volume = 1 - 27/125 = 98/125 of the original. Ratio of upper to lower = 27/125 : 98/125 = 27:98.