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CAT Previous Year Paper | CAT Quants Questions | Question 17

Mensuration is a fairly intuitive topic in CAT Geometry. Other than knowing basic formulae, structural and spatial understanding of the shapes helps one nail Mensuration questions in CAT exam. Mensuration comprises 2D and 3D shapes including (but not limited to) Spheres, Cubes, Cuboids, Cylinders, Cones and more. You can expect at least one question from Mensuration in CAT exam. In this question a right circular cone is cut into two pieces, we have to find the volume of the original cone.

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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