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
- 232
- 256
- 264
- 243
Option: 4
Solution:
Solution:
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 \( = {\left( {\frac{1}{3}} \right)^3}:{1^3} = 1:27\)
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 \( = \frac{{27 \times 225}}{{25}}\) =243 cc.
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