Mensuration
Mensuration
Mensuration covers area, perimeter, surface area, and volume of 2D and 3D shapes. SSC CGL Tier 2 alone carries 4\u20136 questions, making it one of the highest-weightage quant topics. Exams test direct formula application, melting-and-recasting conversions, and fencing/painting cost calculations. Master the scaling rule \u2014 it instantly solves every \u201Cradius increases by x%, find new area\u201D variant.
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
Pick the matching shape formula and plug in dimensions \u2014 most 2D questions are one-step calculations.
3D Volumes
Cube: a³ | Cuboid: lbh | Cylinder: πr²h | Cone: ⅓πr²h | Sphere: (4/3)πr³
Compute volume of any solid object. In melting/recasting problems, equate the old volume to the new shape\u2019s volume and solve for the unknown dimension.
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.