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
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
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
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
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.
Yes, memorizing formulas helps in saving time during exams. Practice regularly using flashcards or formula charts to retain them effectively.
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
Break them into parts. Calculate each shape’s volume or surface area separately, then combine or compare as per the question.
Use formula charts, sticky notes, or mobile flashcards. Revise them daily and test yourself with practice problems.
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