Quantitative Aptitude
Mensuration
Mensuration
Mensuration is the measurement of geometric shapes — area, perimeter, surface area, and volume. Questions involve standard 2D and 3D shapes, cost of fencing/painting, and shape conversions (melting and recasting).
Key Idea
When all linear dimensions are scaled by factor k, area scales by k² and volume by k³. This single rule solves all 'percentage increase in radius → percentage increase in area/volume' problems.
Core Formulas
2D Shapes
Triangle: ½bh (or √s(s−a)(s−b)(s−c)) | Circle: πr², 2πr | Rectangle: lb, 2(l+b) | Trapezium: ½(a+b)h
For area and perimeter of standard flat shapes — identify the shape and apply the right formula.
3D Volumes
Cube: a³ | Cuboid: lbh | Cylinder: πr²h | Cone: ⅓πr²h | Sphere: (4/3)πr³
For volume of solid objects — melting/recasting problems equate volumes of the two shapes.
Surface Areas
Cube: 6a² | Cylinder: 2πr(r+h) | Cone: πr(l+r) where l=√(r²+h²) | Sphere: 4πr²
For painting/coating problems — surface area × rate = cost.
Slant Height of Cone
l = √(r² + h²)
Always compute slant height first before finding lateral surface area of a cone.
Scaling Rule
If dimensions ×k: Area ×k² | Volume ×k³
When radius/side increases by x% — area increases by (2x + x²/100)% and volume by a cube-based factor.
Relevant Exams
Mensuration is one of the highest-weightage topics in SSC CGL Tier 2 — expect 4-6 questions. Cylinder, cone, and sphere conversion problems are especially frequent.