CAT Geometry Mensuration Formulas, Syllabus and Points to Remember

By Aditi Joshi|Updated : January 14th, 2022

Mensuration, a sub-topic of Geometry, appears in the CAT Quantitative Aptitude section. It is an important topic for the CAT exam because this section analyses the diagnostic skills of the candidates to understand geometric figures and shapes. Therefore, the candidates appearing for CAT exam must have knowledge of these topics including cubes, cuboids, spheres, cylinders, cones, lines, coordinate geometry, volume, perimeter, and more.

As per the syllabus, there is a large number of Geometry and mensuration formulas for CAT, therefore most candidates find CAT geometry formulas difficult to remember at exam time. There were around 4-5 questions in CAT on this topic.

So, the aspirants must work towards revising these formulas regularly to have a stronghold on these formulas with an understanding of their applicability.

Table of Content

Syllabus for Geometry and Mensuration for CAT

Geometry and Mensuration for CAT exam include calculations related to various shapes and figures. Mensuration formulas for CAT mainly pertain to the measurement of surface area (both total and curved) and the volumes of solid figures, such as:

  • Cube
  • Cuboid
  • Cone
  • Cylinder
  • Frustum
  • Sphere
  • Pyramid
  • Prism

Additionally, the following topics also are covered in Geometry and Mensuration formulas for the CAT exam.

  • Quadrant System
  • Distance between two lines
  • Concurrent lines and collinear points
  • Equations for lines and circles
  • Supplementary and complementary angle
  • Different types of angles (acute angle, right angle, obtuse angle, isosceles, and equilateral)
  • Different types of Triangles (acute-angled, right-angled, congruent, obtuse-angled)
  • Angular and perpendicular bisector, altitude and median
  • Different geometrical theorems like Pythagoras, Apollonius, inscribed angle, internal and external angular bisector, Midpoint, transversal and Basic proportionality 
  • Cyclic quadrilateral
  • Special triangles
  • Inradius and circumradius
  • Polygon, hexagonal polygon, Rhombus, trapezoid, rectangle, and square

Important Mensuration Formulas for CAT

Before knowing the mensuration formulas for CAT, the candidates must be familiar with some important concepts that are highly recommended for preparing geometry and mensuration for CAT.

  • Length of cuboid and cubical room/ longest rod length
  • The surface of the Pyramid (Measurement of both slant and whole surface)
  • Frustum of a pyramid

Frequently Used Mensuration Formulas for CAT Exam

Geometric Figure

Surface area (total)

Surface area (lateral)

Volume

Slant height/ length of diagonal

Cuboid

2(LB + BH + HL)

2H (L + B)

LBH

√ (L^2 + H^2 + B^2)

Cube

6a^2

4a^2

a^3

√3a

Cone 

πr (r + l)

πrl

πr^2h

√(h^2 + r^2)

Frustum

π(R1 + R2)s + (R1^2 + R2^2)

π(R1 + R2)s

πh(R1^2 + R2^2 + R1R2)

√(h^2 + (R1 – R2)^2)

Cylinder

2πr (r + h)

2πrh

πr^2h

-

Sphere

4πr^2

4πr^2

4/3πr^3

-

Hollow Cylinder

2π(r₁+r₂) (r₂-r₁+h)

2πh(r₁+r₂)

πh(r₂²-r₁²)

-

Hemisphere

3πr^2

2πr^2

2/3πr^3

-

Points to Remember for Geometry and Mensuration for CAT Exam

The candidates should also look after the following points at the time of preparation for Geometry and Mensuration formulas for CAT. 

 Cuboid:

  • It has a length (l), height (h), and breadth (b).

Cube:

  • It has 6 faces.
  • It is a solid figure.
  • Its length, breadth, and height are all equal.

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FAQs

  • No, not at all, but the candidates must have a strong grip on all the formulas related to this section

  • It is not the same every year. The candidates expect 4-5 questions from CAT geometry and mensuration.



  • It is up to you completely, but the suggestion is not to omit this part as it is scoring and also there are around 4-5 (Approx) questions from this section.


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