Mensuration Formulas, Short Tricks, Tips, and Strategies

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Mensuration is one of the most scoring and concept-driven topics in Quantitative Aptitude. Whether it’s a basic question on the area of a square or a complex volume comparison between a cone and a cylinder, having the right formulas at your fingertips makes all the difference.

In competitive exams like SSC, Banking, and RRB, Mensuration questions often appear in direct or applied formats, testing both your conceptual clarity and calculation speed. In this blog, we have covered essential formulas, smart tricks, and proven strategies to help you solve Mensuration questions faster and more accurately, giving you an edge in the exam hall.

What Is Mensuration in Quantitative Aptitude?

Mensuration is the branch of mathematics that deals with the measurement of geometric figures like squares, rectangles, circles, cylinders, cones, and spheres. It involves calculating area, volume, surface area, perimeter, etc.

This topic frequently appears in competitive exams because it tests candidates’ understanding of geometry and practical application skills in real-world measurement problems.

Skills required to solve Mensuration questions:

Geometric visualization
Basic arithmetic speed
Formula application
Unit conversion and interpretation

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Why Is Mensuration Important in Competitive Exams?

Exam	No. of Questions	Difficulty
SSC CGL / CHSL	1–2	Easy
IBPS PO / SBI PO	1–2	Moderate
RRB NTPC / Group D	1	Easy
State PSC / Police	1–2	Moderate

Mensuration is a high-scoring and time-efficient topic if formulas are memorized well.

Mensuration Quantitative Aptitude Short Notes

This section provides quick definitions and explanations of key Mensuration terms.

Term	Explanation
Area	Space inside a 2D figure (measured in sq. units)
Perimeter	Total length of boundary of a 2D shape
Volume	Space occupied by a 3D object (measured in cubic units)
Surface Area	Total area of all faces of a 3D object
Lateral Surface Area	Surface area excluding top and bottom faces
Curved Surface Area	Surface area of the curved part only (e.g., cone or cylinder)
Slant Height	Diagonal height in 3D objects like cone or pyramid

Quick Revision Summary (Flashcard Table)

Use this flashcard-style summary to revise essential Mensuration concepts in one go.

Concept	Explanation
Area of Circle	πr², where r is radius
Volume of Cylinder	πr²h, where r = radius and h = height
Surface Area of Cube	6a², where a is side
Volume of Sphere	(4/3)πr³
CSA of Cone	πrl, where l is slant height
Volume of Cuboid	l × b × h

What Are the Types of Mensuration Questions in Quantitative Aptitude?

Mensuration questions are not always direct formula applications. Competitive exams often frame them in various formats such as real-life applications, comparative shapes, or reverse calculations.

Direct: Straightforward formula-based questions
Application-based: Mixed with real-life scenarios like pipes, tanks, paint
3D Shape Comparison: Relating volume or surface area of one shape with another
Mixed Shape: Two or more figures combined (e.g., cylinder + hemisphere)
Reverse Calculation: Given area/volume, find missing dimension

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Mensuration Formulas for Quantitative Aptitude

Formulas form the core of Mensuration questions. Once you memorize and understand them well, solving questions becomes a matter of seconds. In this section, we provide the detailed list of important area, volume, and surface area formulas for 2D and 3D shapes.

Shape	Area / Volume / Surface Area Formulas
Rectangle	Area = l × b
Square	Area = a²
Circle	Area = πr², Circumference = 2πr
Triangle	Area = ½ × base × height
Trapezium	Area = ½ × (sum of parallel sides) × height
Cylinder	Volume = πr²h, CSA = 2πrh, TSA = 2πr(h + r)
Cone	Volume = ⅓πr²h, CSA = πrl, TSA = πr(l + r)
Sphere	Volume = (4/3)πr³, Surface Area = 4πr²
Hemisphere	Volume = (2/3)πr³, CSA = 2πr², TSA = 3πr²
Cube	Volume = a³, TSA = 6a², LSA = 4a²
Cuboid	Volume = l × b × h, TSA = 2(lb + bh + hl), LSA = 2h(l + b)

Mensuration Tricks for SSC CGL and Other Exams

Speed and accuracy are key in exams like SSC, IBPS, and RRB. This section shares time-saving tips and smart strategies that will help you solve Mensuration questions faster.

Memorize area and volume formulas as grouped sets (2D vs 3D).
Use π = 22/7 unless specified.
Always check if dimensions are in the same unit.
For paint/fencing type questions, focus on perimeter or area only.
In tank-pipe scenarios, volume is the key; for wrapping/painting, use surface area.
For comparative shape questions, equate volumes or surface areas directly.
Convert compound shapes into basic components.

Solved Mensuration Questions from 2024–25 Exams

Asked in SSC CGL 2024 Tier 1 Shift 2 (Memory-Based)

Q1. The radius of a cylinder is 7 cm, and height is 10 cm. Find its volume.
Answer: πr²h = (22/7) × 7 × 7 × 10 = 1540 cm³

From IBPS PO Prelims 2024

Q2. Find the surface area of a cube of side 6 cm.
Answer: TSA = 6a² = 6 × 36 = 216 cm²

Asked in RRB NTPC 2024

Q3. Area of a square is 144 cm². What is its perimeter?
Answer: Side = √144 = 12 cm → Perimeter = 4 × 12 = 48 cm

Questions

Q4. A hemisphere of radius 7 cm is melted and converted into a cone of height 7 cm. Find the radius of the cone.
Answer:
Volume of hemisphere = Volume of cone
(2/3)πr³ = (1/3)πR²h
Solving: R² = 2r³/h → R² = 2×343/7 = 98 → R = √98 ≈ 9.9 cm

Mensuration Concepts for Bank Exams

In IBPS and SBI exams, Mensuration questions may involve:

Cylinders and cones with painted areas
Symbol-based dimensions (like x cm, y cm)
Questions involving cost estimation for painting/wrapping a surface

Example:
A pipe is cylindrical in shape with radius x and height y. Find its surface area in terms of x and y.
→ Answer: CSA = 2πxy

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Common Mistakes to Avoid while Solving Mensuration

While solving Mensuration Quantitative Aptitude questions, candidates must keep the below mentioned details in mind:

Mixing up surface area and lateral surface area
Using wrong value of π
Ignoring unit conversion
Incorrect formula substitution
Overlooking dimensions given in different units (cm, m, etc.)

What Are Related Topics I Should Revise Next?

Topics you should revise next are as follows:

Questions based on Time and Distance
Rules and Practice Questions of Simplification
Shortcuts and Patterns of Number Series
Various types of Questions Based on Data Interpretation
Tricks & Examples of Inequalities

FAQs

Q1. What are the most important formulas to remember for Mensuration?

You must remember area and volume formulas for shapes like square, rectangle, circle, cylinder, cone, sphere, cube, and cuboid. Surface area and curved surface area formulas are also essential.

Q2. Is it necessary to memorize all Mensuration formulas?

Yes, memorizing formulas helps in saving time during exams. Practice regularly using flashcards or formula charts to retain them effectively.

Q3. How to handle unit conversion in Mensuration?

Always convert all dimensions to the same unit (like cm or m) before applying formulas. Know that:
1 m = 100 cm,
1 cm² = 0.0001 m²,
1 m³ = 1000000 cm³

Q4. How to approach compound shape questions (e.g., cone on a cylinder)?

Break them into parts. Calculate each shape’s volume or surface area separately, then combine or compare as per the question.

Q5. What is the best way to memorize Mensuration formulas?

Use formula charts, sticky notes, or mobile flashcards. Revise them daily and test yourself with practice problems.

AditiOB

Hi, I’m Aditi. I work as a Content Writer at Oliveboard, where I have been simplifying exam-related content for the past 4 years. I create clear and easy-to-understand guides for JAIIB, CAIIB, and UGC exams. My work includes breaking down notifications, admit cards, and exam updates, as well as preparing study plans and subject-wise strategies.
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