Volume & Surface Areas
📋 Quick-reference guides with key formulas and must-know concepts. Perfect for daily practice, last-minute revision, and on-the-go learning.
Cheat Sheets
Study MaterialVolume & Surface Areas Cheat Sheet
Volume and Surface Areas is one of the most important and frequently asked topics in Quantitative Aptitude and Mensuration for SSC, Banking, Railway, UPSC, Defence, Insurance, CAT, and other competitive examinations.
This cheat sheet helps candidates understand formulas of three-dimensional figures, volume and surface area calculations, melting and recasting concepts, water flow problems, and shortcut techniques for solving mensuration-based questions quickly and accurately in exams.
About This Cheat Sheet
Complete guide to Volume and Surface Areas for competitive exams:
Basic Concepts
- Volume of Solids
- Surface Area Concepts
- Curved Surface Area
- Total Surface Area
Cube & Cuboid
- Volume Formulas
- Surface Area Formulas
- Diagonal Concepts
- Dimension Change Problems
Cylinder & Hollow Cylinder
- Volume Calculations
- Curved Surface Area
- Total Surface Area
- Pipe & Hollow Shape Problems
Cone & Frustum
Volume, slant height, surface area, and frustum calculations.
Sphere & Hemisphere
- Volume Formulas
- Surface Area Formulas
- Curved Surface Area
- Ratio Based Problems
Combination of Solids
- Combined Shapes
- Melting & Recasting
- Shape Conversion
- Number of Smaller Objects
Practical Applications
- Water Flow Problems
- Cost Based Problems
- Ratio of Volumes
- Dimension Variation Effects
Shortcut Tricks
Fast solving methods, mensuration shortcuts, and exam-oriented geometry techniques.
Topics Covered
| Topic | Description |
|---|---|
| Cube | Volume = a³, Surface Area = 6a² |
| Cuboid | Volume = l×b×h |
| Cylinder | Volume and curved surface area formulas |
| Hollow Cylinder | Volume and surface area of hollow pipes |
| Cone | Volume, slant height, and surface area |
| Frustum of Cone | Volume and area calculations |
| Sphere | Volume = (4/3)πr³ |
| Hemisphere | Volume and curved surface area formulas |
| Combination of Solids | Problems involving combined shapes |
| Melting & Recasting | Conversion of one solid into another |
| Water Flow Problems | Volume and time relation in pipes |
| Ratio Problems | Volume and surface area comparisons |
| Cost Problems | Painting, polishing, and filling costs |
| Shortcut Tricks | Fast solving methods for exams |
Why This Cheat Sheet is Important
Understand 3D Mensuration Concepts
↓
Improve Formula Application Skills
↓
Apply Shortcut Techniques
↓
Solve Geometry Problems Faster
↓
Score Better in Exams
Competitive Exams Covered
- SSC CGL
- SSC CHSL
- Bank PO & Clerk
- Railway Exams
- UPSC CSAT
- Defence Exams
- Insurance Exams
- State Government Exams
- MBA Entrance Exams
Quick Examples
Example 1:
Find the volume of a cube having side 6 cm.
Volume = a³
= 6³
= 216 cm³
Example 2:
Find the total surface area of a cuboid having length 8 cm, breadth 5 cm, and height 4 cm.
TSA = 2(lb + bh + hl)
= 2(8×5 + 5×4 + 8×4)
= 2(40 + 20 + 32)
= 184 cm²
Example 3:
Find the curved surface area of a cylinder having radius 7 cm and height 10 cm.
CSA = 2Ï€rh
= 2 × 22/7 × 7 × 10
= 440 cm²
Example 4:
Find the volume of a sphere having radius 3 cm.
Volume = (4/3)πr³
= (4/3) × 22/7 × 3³
≈ 113.14 cm³
Example 5:
A metal cube of side 6 cm is melted and recast into small cubes of side 2 cm. Find the number of small cubes formed.
Number of cubes =
(6³)/(2³)
= 216/8
= 27
Answer = 27 cubes
Final Takeaway
This Volume & Surface Areas Cheat Sheet provides complete revision material for all major concepts frequently asked in competitive examinations. Regular practice of mensuration formulas, melting and recasting problems, water flow concepts, and shortcut techniques can significantly improve speed, accuracy, and geometry problem-solving ability.
It is highly useful for quick revision before exams and helps candidates strengthen the foundation of Quantitative Aptitude.
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