Mensuration
Delhi Police Exam
1. What is Mensuration?
Mensuration is the branch of mathematics that deals with measuring geometric figures — their length, area, and volume.
In exams like Delhi Police, Mensuration questions usually involve 2D shapes (plane figures) and 3D solids.
2D Shapes - Plane Figures
3D Solids - Spatial Figures
Simple Definition:
Mensuration = Calculating Perimeter, Area, Surface Area, or Volume of geometric shapes.
Examples:
| Shape | Quantity Measured |
|---|---|
| Square | Area, Perimeter |
| Rectangle | Area, Perimeter |
| Circle | Area, Circumference |
| Triangle | Area, Perimeter |
| Cylinder | Surface Area, Volume |
| Sphere | Surface Area, Volume |
| Cone | Surface Area, Volume |
2. Basic Formulas for 2D Figures
| Shape | Perimeter | Area |
|---|---|---|
| Square | 4a | a² |
| Rectangle | 2(l + b) | l × b |
| Triangle | a + b + c | √[s(s–a)(s–b)(s–c)] s = (a+b+c)/2 |
| Circle | 2πr | πr² |
| Parallelogram | 2(a+b) | b × h |
| Trapezium | a + b + c + d | ½ × (sum of parallel sides) × height |
Shortcuts:
Perimeter → Sum of all sides
Area → Base × Height (for rectangle, triangle, parallelogram)
Circle → Use π ≈ 3.14 or 22/7
3. Basic Formulas for 3D Solids
| Solid | Surface Area | Volume |
|---|---|---|
| Cube | 6a² | a³ |
| Cuboid | 2(lb + bh + hl) | l × b × h |
| Sphere | 4πr² | 4/3 πr³ |
| Hemisphere | 3πr² | 2/3 πr³ |
| Cylinder | 2πr(h + r) | πr²h |
| Cone | πr(l + r) | 1/3 πr²h |
4. Key Concepts & Tricks
| Concept | Trick / Shortcut |
|---|---|
| Diagonal of square | d = a√2 |
| Diagonal of rectangle | d = √(l² + b²) |
| Volume of cube/cuboid | Product of dimensions |
| Surface area | Sum of all faces (cube/cuboid) or curved + base (cylinder/cone) |
| Sphere radius from volume | r = (3V/4π)1/3 |
5. Conversion & Units
Length
m, cm, mm, km
Area
m², cm², mm²
Volume
m³, cm³, litres
Important Conversions:
1 m³ = 1000 litres
1 litre = 1000 cm³
6. Real-Life Analogy
Area
Carpet needed for a floor
Perimeter
Fencing around a garden
Volume
Water a tank can hold
Surface Area
Paint needed for a wall or box
7. Common Delhi Police / SSC Exam Facts
Focus on quick formulas and approximation
Most frequent figures: Square, Rectangle, Circle, Cylinder, Cube, Sphere, Cone
Always check units — convert to same unit before calculation
Questions often combine 2D and 3D shapes
8. Practice Questions (Exam-Type)
| No. | Question | Solution | Answer |
|---|---|---|---|
| 1 | Area of rectangle 10×5 | 10×5 = 50 | 50 |
| 2 | Perimeter of square side 6 | 4×6 = 24 | 24 |
| 3 | Volume of cube side 4 | 4³ = 64 | 64 |
| 4 | Curved surface area of cylinder r=7, h=10 | 2πrh = 2×22/7×7×10 = 440 | 440 |
| 5 | Surface area of sphere r=5 | 4πr² = 4×3.14×25 = 314 | 314 |
9. Quick Recap
| Concept | Summary |
|---|---|
| Area | Space inside 2D figure |
| Perimeter | Boundary length of 2D figure |
| Surface Area | Total area of 3D solid faces |
| Volume | Space occupied by 3D solid |
| Key Formulas | Cube, Cuboid, Cylinder, Cone, Sphere |
| Shortcut | Diagonals, curved surfaces, base areas |
You've completed Mensuration Concepts!
Courage Tip: Remember the key formulas for area, perimeter, surface area, and volume. Practice unit conversions and focus on frequently asked shapes like cubes, cylinders, and spheres for Delhi Police exams.
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