Question

A solid right circular cone of height 27 cm is cut into two pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

• A. 232
• B. 256
• C. 264
• D. 243

Answer 1

Answer: (D)

243

Answer 2

As the cone is cut at one-third height from the top (the vertex), the total volume is proportional to the cubes of the heights of the two parts.

Ratio of volumes two parts = $\bigg(\frac{1}{3}\bigg)^3:13 = 1:27$

Hence the bottom part will have volume of $27 - 1$i.e., $26$ parts.

Given $(26 -1)$ i.e., $25$ parts $-225$ cc.

Hence the required answer is $27$ parts = $\frac{27×225}{25} = 243$ cc.

So, the correct answer is (D): $243$