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Question 17 : A solid right circular cone of height 27 cm is cut into 2 pieces along a plane parallel to it's base at a height of 18 cm from the base. If the difference in the volume of the two pieces is 225 cc, the volume, in cc, of the original cone is

  1. 264
  2. 232
  3. 243
  4. 256

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Explanatory Answer

When we consider top part of the triangle
Height is = \\frac{1}{3})rd of original height
Right Circular Cone
If height becomes \\frac{1}{3})rd then radius also becomes \\frac{1}{3})rd
If both height and radius become \\frac{1}{3})rd, Volume will be \\frac{1}{27})th
So, Top part’s volume = V
Remaining part = 26V
Totally = 27V
Given 26 V – V = 225
V = 9
27 V = 243

The answer is, "243"

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