Lesson 1.9: Mensuration & Geometry
Introduction:
Mensuration and geometry questions are common in SSC exams, especially in CGL and CHSL quantitative aptitude. These questions test your knowledge of areas, volumes, and basic geometric properties.
1. Mensuration
a) Area of Plane Figures
| Shape | Formula |
|---|---|
| Square | Area=a2\text{Area} = a^2 |
| Rectangle | Area=l×b\text{Area} = l \times b |
| Triangle | Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} |
| Parallelogram | Area=base×height\text{Area} = \text{base} \times \text{height} |
| Trapezium | Area=12(a+b)×h\text{Area} = \frac{1}{2} (a+b) \times h |
| Circle | Area=πr2\text{Area} = \pi r^2 |
b) Volume & Surface Area of Solids
| Solid | Volume | Surface Area |
|---|---|---|
| Cube | a3a^3 | 6a26a^2 |
| Cuboid | l×b×hl \times b \times h | 2(lb+bh+hl)2(lb + bh + hl) |
| Sphere | 43πr3\frac{4}{3} \pi r^3 | 4πr24 \pi r^2 |
| Cylinder | πr2h\pi r^2 h | 2πr(h+r)2 \pi r(h+r) |
| Cone | 13πr2h\frac{1}{3} \pi r^2 h | πr(l+r)\pi r(l+r) |
Note: l=slantheight,r=radius,h=height,a=sidel = slant height, r = radius, h = height, a = side
2. Geometry Basics
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Triangle: Sum of angles = 180°
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Quadrilateral: Sum of angles = 360°
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Circle: Circumference = 2πr2\pi r, Area = πr2\pi r^2
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Pythagoras Theorem: a2+b2=c2a^2 + b^2 = c^2 for right-angled triangle
Example 1:
A rectangle has length 10 m and breadth 6 m. Area = 10 × 6 = 60 m²
Example 2:
A cylinder with radius 7 cm and height 10 cm. Volume = πr2h=3.1416×49×10≈1539.38 cm³\pi r^2 h = 3.1416 × 49 × 10 ≈ 1539.38 \, \text{cm³}
3. SSC Exam Tips
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Memorize formulas for quick recall.
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Focus on commonly asked shapes: square, rectangle, triangle, circle, cube, cuboid, cylinder.
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Practice shortcut methods for circumference, area, and volume.
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Check units carefully (m², cm², m³, cm³).
4. Practice Questions
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Find the area of a triangle with base 12 cm and height 9 cm.
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Volume of a cuboid with length 10 m, breadth 5 m, height 3 m.
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Surface area of a sphere with radius 7 cm.
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Circumference and area of a circle with radius 14 cm.
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A cylinder has radius 5 cm and height 12 cm. Find its volume and surface area.