Study Notes: Mensuration

**SSC General Duty Constable — Elementary Mathematics**

Overview

Mensuration questions form a core part of the SSC GD mathematics section, typically contributing 3–5 questions per paper. This topic tests your ability to calculate areas, perimeters, surface areas, and volumes of common two-dimensional and three-dimensional shapes. Most problems are formula-based with straightforward numerical substitution, though some require two-step reasoning (for example, finding the radius first before calculating area).

For SSC GD, you must be thoroughly familiar with triangles, quadrilaterals (especially rectangles, squares, parallelograms, and trapeziums), circles, and common 3-D solids like cubes, cuboids, cylinders, cones, and spheres. Questions are often set in practical contexts—painting walls, filling tanks, fencing fields, or wrapping boxes—which makes unit awareness crucial. A single formula error or unit mismatch can cost you marks, so accuracy with standard formulas is non-negotiable.

The key to scoring well in mensuration is memorizing the correct formulas, practicing unit conversions (metres to centimetres, square metres to square centimetres), and drilling enough problems to recognize which formula applies instantly. Since SSC GD allows calculators in some shifts (verify your specific instructions), speed matters as much as accuracy.

Key Concepts

• **Area** measures the surface enclosed by a 2-D figure, expressed in square units (cm², m², etc.). Perimeter measures the boundary length, expressed in linear units (cm, m, etc.).
• **Surface area** of a 3-D object is the total area covering all its outer faces. **Volume** measures the space inside a 3-D object, expressed in cubic units (cm³, m³, litres).
• For **composite figures** (e.g., a path around a rectangle, or a figure made of a rectangle and semicircle), break the shape into simpler parts and add or subtract areas as needed.
• **Diagonal** of a rectangle = √(length² + breadth²). Diagonal of a square with side *a* = *a*√2. These often appear as intermediate steps in multi-step problems.
• The ratio of the **circumference of a circle to its diameter** is π (pi), approximately 22/7 or 3.14. Most SSC GD problems use π = 22/7 unless stated otherwise.
• For cylinders, cones, and spheres, **radius (r)** is half the diameter. Confusing radius with diameter is a frequent source of error—always double-check what the question provides.
• When a problem mentions "four walls" of a room, you calculate the **lateral surface area** (exclude floor and ceiling). If it says "whole room," include all six faces.
• **Unit conversions**: 1 m = 100 cm, so 1 m² = 10,000 cm² and 1 m³ = 1,000,000 cm³. Also, 1 litre = 1000 cm³. Always convert to a common unit before calculating.

Formulas / Key Facts

**Two-Dimensional Figures**