Hello Students,
I am Rahul Sir, and today we will discuss one of the most important topics in quantitative aptitude for IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, RBI Assistant, and other banking examinations—Volume and Surface Area.
Questions from this topic are regularly asked in arithmetic sections because they test your understanding of geometry, formulas, calculation speed, and application skills. Many aspirants find these questions difficult because they involve multiple formulas for cubes, cuboids, cylinders, cones, and spheres. However, once you understand the concepts and learn a few shortcut techniques, solving these questions becomes much easier.
In banking exams, questions are generally based on direct formula application, comparison of volumes, water filling problems, hollow containers, and surface area calculations. A strong command over formulas and calculation tricks can help you score quickly with high accuracy.
In this article, I will explain important concepts, formulas, shortcuts, common mistakes, and solved examples that will help you master Volume and Surface Area questions for competitive exams.
1. Understanding Volume and Surface Area Basics
Volume refers to the space occupied by a three-dimensional object, whereas surface area represents the total area covered by the outer surfaces of the object.
Common 3D figures asked in exams include:
- Cube
- Cuboid
- Cylinder
- Cone
- Sphere
- Hemisphere
The first step to solving these questions is identifying the shape correctly.
Important Formulas
| Shape | Volume |
|---|---|
| Cube | a³ |
| Cuboid | l × b × h |
| Cylinder | πr²h |
| Cone | (1/3)πr²h |
| Sphere | (4/3)πr³ |
Example
A cube has side 5 cm.
Volume = 5³ = 125 cm³
Many students memorize formulas but fail to understand their applications. Banking exams often twist questions by changing dimensions or comparing volumes.
Quick Tip
Always write the formula before starting calculations. This reduces mistakes and increases accuracy.
2. Important Cube and Cuboid Questions
Cube and cuboid problems are among the most frequently asked questions in aptitude exams.
Cube Formulas
Volume = a³
Total Surface Area = 6a²
Diagonal = a√3
Cuboid Formulas
Volume = l × b × h
TSA = 2(lb + bh + hl)
Diagonal = √(l²+b²+h²)
Example
A cuboid has dimensions:
Length = 8 cm
Breadth = 6 cm
Height = 5 cm
Volume = 8 × 6 × 5
= 240 cm³
Shortcut
If each edge of a cube increases by 10%, volume increases by:
(1.1)³
= 1.331
= 33.1%
This shortcut is extremely useful in percentage-based geometry questions.
Exam Strategy
Memorize all cube and cuboid formulas because they form the foundation for advanced volume and surface area problems.
3. Cylinder-Based Questions and Tricks
Cylinder questions are very common in IBPS and SBI examinations.
Formula
Volume = πr²h
Curved Surface Area = 2πrh
Total Surface Area = 2πr(r+h)
Example
Radius = 7 cm
Height = 10 cm
Volume = (22/7) × 7 × 7 × 10
= 1540 cm³
Shortcut
Use π = 22/7 whenever radius is divisible by 7.
Use π = 3.14 when decimals are involved.
Common Exam Pattern
- Water stored in cylindrical tank
- Comparing capacities
- Increase in radius or height
Quick Trick
Volume depends on r².
If radius doubles:
New Volume = 2² = 4 times
Understanding such proportional relationships helps solve questions quickly without lengthy calculations.
4. Cone and Frustum Questions
Cones are another important topic.
Formula
Volume = (1/3)πr²h
Curved Surface Area = πrl
where l is slant height.
Example
Radius = 6 cm
Height = 9 cm
Volume
= (1/3) × (22/7) × 36 × 9
= 339.43 cm³
Shortcut
Cone volume is always one-third of a cylinder with the same radius and height.
Example
Cylinder Volume = 600 cm³
Cone Volume = 200 cm³
This shortcut saves significant time during exams.
Important Concept
Questions may compare cone and cylinder capacities. Understanding the one-third relationship helps solve them instantly.
5. Sphere and Hemisphere Problems
Sphere questions are generally formula-based.
Formula
Sphere Volume
= (4/3)πr³
Surface Area
= 4πr²
Hemisphere Volume
= (2/3)πr³
Example
Radius = 3 cm
Volume
= (4/3) × (22/7) × 27
= 113.14 cm³
Shortcut
If radius doubles:
Volume increases by
2³ = 8 times
Surface Area increases by
2² = 4 times
These concepts frequently appear in comparative aptitude questions.
Exam Tip
Always remember:
Volume depends on cube of radius.
Surface area depends on square of radius.
6. Water Filling and Capacity Questions
These questions are highly important for banking exams.
Example
A tank has dimensions:
Length = 10 m
Breadth = 5 m
Height = 2 m
Capacity
= 10 × 5 × 2
= 100 m³
Since
1 m³ = 1000 litres
Capacity
= 100,000 litres
Shortcut
Remember:
| Unit | Conversion |
|---|---|
| 1 m³ | 1000 litres |
| 1000 cm³ | 1 litre |
Common Questions
- Tank filling
- Water overflow
- Capacity comparison
- Pipe-related volume
Knowing unit conversions can save valuable exam time.
7. Surface Area Concepts and Tricks
Surface area questions test understanding of exposed surfaces.
Cube Example
Side = 4 cm
Total Surface Area
= 6 × 4²
= 96 cm²
Cuboid Example
Length = 5
Breadth = 4
Height = 3
TSA
= 2(20 + 12 + 15)
= 94 cm²
Shortcut
If cube side doubles:
Surface Area becomes
2² = 4 times
Common Questions
- Painting walls
- Covering boxes
- Cost of polishing
- Wrapping objects
These questions often combine arithmetic and geometry concepts.
8. Percentage Change in Volume and Surface Area
This is one of the favorite areas of examiners.
Shortcut Formula
Percentage Change in Volume
≈ 3 × Percentage Change in Side
(for small changes)
Example
Side increases by 5%
Volume increase
≈ 15%
Actual
(1.05)³
= 15.76%
Surface Area
Percentage Change
≈ 2 × Percentage Change in Side
Side increases by 10%
Surface Area increases by approximately 20%
These shortcuts reduce calculation time drastically.
9. Common Mistakes to Avoid
Many students lose marks because of avoidable mistakes.
Mistake 1
Confusing surface area with volume formulas.
Mistake 2
Incorrect use of π.
Mistake 3
Ignoring unit conversions.
Mistake 4
Using diameter instead of radius.
Mistake 5
Calculation errors in squaring and cubing.
Example
Radius = 5 cm
Students often use:
5² = 10
Incorrect
Correct:
5² = 25
Prevention Strategy
- Write formulas clearly.
- Check units.
- Verify radius and diameter.
- Recheck multiplication.
Small corrections can improve accuracy significantly.
10. Exam-Oriented Practice Strategy
Success in volume and surface area depends on regular practice.
Daily Plan
Week 1
- Learn all formulas.
- Solve basic questions.
Week 2
- Practice mixed geometry questions.
Week 3
- Attempt previous year banking papers.
Week 4
- Solve sectional mocks.
Recommended Target
- 20 questions daily
- 3 mock tests weekly
- Formula revision every weekend
Speed Trick
Create a formula chart and revise it every day for 10 minutes.
Consistent practice helps recognize question patterns quickly and boosts confidence during exams.
How Teachers from OdTutor Can Help
At ODTutor, experienced aptitude trainers provide structured coaching for IBPS PO, IBPS Clerk, SBI, RBI, SSC, Railways, and other competitive examinations. Our teachers focus on conceptual clarity, shortcut techniques, exam-oriented practice, mock tests, and doubt-solving sessions. Students receive personalized guidance on topics like Volume and Surface Area, Percentage, Profit and Loss, Time and Work, Data Interpretation, and Reasoning. Through live classes, recorded lectures, practice assignments, and performance analysis, ODTutor helps aspirants improve speed, accuracy, and confidence. Whether you are a beginner or an advanced learner, ODTutor’s expert faculty can help you achieve your banking exam goals effectively.