Quick Tips on How to Prepare Mensuration for CDS Exam

By Akanksha Jigyasu|Updated : March 23rd, 2022

Mensuration basically means 'Measurement' and this segment of Elementary mathematics involves the measurement of areas, volumes, lengths etc of the given figures. In this post, we have covered some important tips to prepare Mensuration for the CDS exam. 

Out of the 100 questions of the Mathematics section, mensuration usually accounts for 12-15 questions in the CDS exam and hence, one must be thorough with the concepts and important formulas of Mensuration for the CDS exam, to score well in its Mathematics section.

So, understand these Mensuration preparation tips for the Combined Defence Services exam now, along with the commonly used formulas of Mensuration in CDS & enhance your Maths score!

How to Prepare Mensuration for CDS Exam?

Mensuration can be broadly categorized into 2 segments, namely:
(a) 2-D Mensuration
(b) 3-D Mensuration

As the name suggests, 2-D Mensuration deals with the computation of areas/ volumes/ lengths of 2-dimensional figures like Squares, Rectangles, Rhombus, Circle, Parallelogram, Trapezium etc while 3D mensuration is for figures like Cubes, Cuboids, Cone, Cylinder, Sphere etc.
In order to solve the questions of Mensuration for the CDS exam, one must be well-versed with its commonly used formulas. We will now cover both 2D & 3D Mensuration for the CDS exam.

Important formulas for 2-D Mensuration

Figure & its Diagram

Commonly Used Formulas

1. Rectangle


(a) Area = l x b

(b) Perimeter = 2 (l + b)

(c) Length of Diagonal = √l2 + b2

2. Square

(a) Area = a2

(b) Perimeter = 4*a

(c) Length of Diagonal = a*√2

3. Parallelogram

(a) Area = l x h

(b) Perimeter = 2*(l + b)

4. Triangle

(a) Area of right-angled triangle = ½ *b*h

(b) Area of Scalene triangle (sides a, b, c) =
s = (a + b + c)/ 2 (s = semi-perimeter)
Area = √ {s (s-a) (s-b) (s-c)}

(c) Area of Isosceles triangle
= b/4 *√(4a2 – b2)

(d) Area of Equilateral triangle
= √3/4 * a2

5. Trapezium

(a) Area = ½*(AB + CD)*AE

(b) Perimeter = Sum of all sides

6. Rhombus

(a) Area = ½ *(Product of diagonals) = ½d1d2

(b) Perimeter = 4*l

7. Circles

(a) Area = πr2

(b) Circumference = 2πr 

(c) Length of Arc AB = (2πrθ)/360
(where θ is the angle at the centre)

(d) Area of sector AOB
= (1/2) × (length of arc) × r = (πr2θ)/360

Important Formulas for 3-D Mensuration

Figure & its Diagram

Commonly Used Formulas

1. Cube

(a) Volume = a3

(b) Total Surface Area = 6a2

(c) Length of diagonal through centre = a*√3

2. Cuboid

(a) Volume = l*b*h

(b) Total Surface Area = 2*(lb + bh + hl)

(c) Length of diagonal through centre
= √l2 + b2 + h2

3. Cone

(a) Volume = 1/3 * πr2h

(b) Total Surface Area = π*r*(l + r)

(c) Curved Surface Area = π*r*l

(d) Slant height = √(h2+r2)

4. Cylinder

(a) Volume = πr2h

(b) Total Surface Area = 2πr*(h + r)

(c) Curved Surface Area = 2πrh

5. Sphere & Hemisphere

(a) Volume of Sphere = (4/3) πr3
(b) Surface area of Sphere = 4πr2
(c) Volume of Hemisphere = (2/3) *πr3
(d) Total Surface area of Hemisphere = 3πr2
(e) Curved Surface Area of Hemisphere = 2πr2

Download Important Formula PDF

General Tips while solving Mensuration Questions in the CDS exam:

  • Avoid doing the complete calculations at each & every step. A number of values, say radius, height etc cancel out each other while equating the values in either step of the question. So, minimize your calculations wherever possible.
  • Go for shortcuts only if you have a very thorough practice of the questions of Mensuration. Else, mugging up the shortcuts will unnecessarily confuse you in the exam.
  • Calculate carefully! The values given in the questions may be in decimal or may have complex calculations. So, be very careful while working with them to avoid silly errors.
  • Practice all the variations of Mensuration questions, while are available in a number of mathematics books to familiarise yourself with the type of questions that may come up in the CDS exam.
    For instance, questions involving computation of fencing/ flooring/ painting cost, questions involving percentage increase/ decrease in either of their parameter like length, breadth, height etc., questions where one figure is inscribed within another figure etc.

Remember, there is nothing that you can’t achieve with proper dedication. So, practice the questions of different topics regularly, in order to enhance your calculation speed & work on your comfort level as far as these questions are concerned.

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write a comment
Kartik Sharma
well explained
Suraj Shinde

Suraj ShindeSep 21, 2021

8788308430 प्लीज हेल्प. एम पी एस सी साठी 


  • CDS Exam consists of 3 papers which are English, General Knowledge, Mathematics.

  • For OTA, the candidate has to take an English & General Knowledge Paper.

  • Yes, there is a negative marking in the CDS Exam, 0.33 marks for every wrong answer.

  • All the Candidates who clear the CDS Exam are called for SSB Interviews.

  • There is no restriction on the number of attempts if you are fulfilling the age criteria.

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tags :CDS & Defence ExamsElementary MathematicsCDS OverviewCDS Apply OnlineCDS VacancyCDS Eligibility CriteriaCDS Selection Process

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