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

- 264
- 232
- 243
- 256

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When we consider top part of the triangle

Height is = \\frac{1}{3})rd of original height

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

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