Mensuration — RRB NTPC Study Notes

Overview

Mensuration is the quantitative study of geometric figures — computing area, perimeter, surface area and volume. For RRB NTPC, this topic consistently delivers 2–4 direct questions each year, making it a high-yield area. Questions test both formula recall and the ability to apply formulas to word problems involving real-world objects like water tanks, metal sheets, ground plots, and packaging.

Mastery means knowing the right formula instantly and executing arithmetic cleanly. Most errors come from unit confusion (mixing cm and m), incorrect formula selection (lateral vs. total surface area), or algebraic slips when solving for an unknown dimension. Since mensuration questions are computation-heavy, speed and accuracy in multiplication, squaring, and handling π are critical.

The syllabus explicitly covers 2-D shapes (triangle, rectangle, square, circle, trapezium) and 3-D solids (cube, cuboid, cylinder, cone, sphere, hemisphere). You won't see complex composite solids, but do expect problems combining two shapes or converting between volume and capacity (1 litre = 1000 cm³).

Key Concepts

• **Area** measures the space inside a 2-D boundary; units are always square (cm², m², etc.). Perimeter measures the boundary length itself.
• **Surface area** for 3-D solids comes in two flavors: **lateral (curved) surface area** excludes the top/bottom bases; **total surface area** includes all faces.
• **Volume** measures the space a 3-D object occupies; units are cubic (cm³, m³). One cubic metre = 1000 litres; one litre = 1000 cm³.
• The number **π (pi)** appears in all circular formulas. Use π = 22/7 or 3.14 as instructed; RRB typically accepts 22/7 unless specified otherwise.
• For composite figures, break them into standard shapes, compute each separately, then add or subtract areas/volumes as needed.
• Always convert units to a common system before calculating. Mixing metres and centimetres is the #1 source of wrong answers.
• The diagonal of a rectangle with sides a and b is √(a² + b²); for a cube of side a, space diagonal = a√3.
• Heron's formula for triangle area works when three sides are known but no height is given: use the semi-perimeter method.

Formulas / Key Facts

**2-D Figures**

• **Rectangle**: Area = length × breadth; Perimeter = 2(length + breadth)
• **Square**: Area = side²; Perimeter = 4 × side; Diagonal = side√2
• **Triangle**: Area = ½ × base × height; Heron's formula: Area = √[s(s−a)(s−b)(s−c)] where s = (a+b+c)/2
• **Circle**: Area = πr²; Circumference = 2πr; where r = radius
• **Semicircle**: Area = πr²/2; Perimeter = πr + 2r (curved part + diameter)
• **Trapezium**: Area = ½ × (sum of parallel sides) × height