Mensuration Questions for SSC CGL: What This Set Covers
This page has 20 original SSC-style mensuration questions with solutions, split into 2D figures (triangle, quadrilateral, circle, regular polygon) and 3D solids (cube, cuboid, cylinder, cone, sphere, hemisphere, prism, pyramid), plus a short set on percentage change and melting/recasting, the two twists SSC adds most often. The SSC CGL 2026 notice lists "Triangle, Quadrilaterals, Regular Polygons, Circle, Right Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular Parallelepiped, Regular Right Pyramid with triangular or square base" in the Tier 1 Quantitative Aptitude syllabus (para 13.10.3), and the same list under "Mensuration" in the Tier 2 Mathematical Abilities syllabus (para 13.11.1.5).
Why now (as of 7 November 2026): SSC CGL Tier 2 is tentatively in December 2026 (CGL 2026 notice) and SSC CHSL Tier 1 runs 30 November–31 December 2026 (SSC notice dated 01.10.2026). Mensuration is formula-driven, so a week of drilling turns it into reliable marks.
Keep Mensuration Formulas for SSC CGL open for the full formula list; this page is the practice set. Use π = 22/7 unless the question says otherwise.
The 10 Formulas This Set Uses
| Figure | Formula |
|---|---|
| Equilateral triangle (side a) | Area = (√3/4)a² |
| Any triangle (sides a, b, c) | Heron: √[s(s − a)(s − b)(s − c)], s = (a + b + c)/2 |
| Rhombus (diagonals d₁, d₂) | Area = d₁d₂/2; side = √[(d₁/2)² + (d₂/2)²] |
| Circle / sector (angle θ) | Area πr²; sector = (θ/360)πr²; arc = (θ/360)2πr |
| Regular hexagon (side a) | Area = (3√3/2)a² |
| Regular polygon | Exterior angle = 360°/n |
| Cuboid l × b × h | Diagonal = √(l² + b² + h²) |
| Cylinder / cone | V = πr²h / (1/3)πr²h; cone CSA = πrl, l = √(r² + h²) |
| Sphere / hemisphere | V = (4/3)πr³; hemisphere TSA = 3πr² |
| Pyramid | Lateral surface = ½ × base perimeter × slant height |
Set A: 2D Figures (Q1–Q7)
Q1. Find the area of an equilateral triangle of side 12 cm. (a) 36√3 cm² (b) 48√3 cm² (c) 72 cm² (d) 144√3 cm² Answer: (a). (√3/4) × 144 = 36√3.
Q2. Find the area of a triangle with sides 13 cm, 14 cm and 15 cm. (a) 72 cm² (b) 84 cm² (c) 91 cm² (d) 96 cm² Answer: (b) 84. s = 21; √(21 × 8 × 7 × 6) = √7056 = 84. Remember the 13-14-15 triangle: SSC repeats it.
Q3. The diagonals of a rhombus are 16 cm and 12 cm. Find its perimeter. (a) 28 cm (b) 36 cm (c) 40 cm (d) 48 cm Answer: (c) 40. Half-diagonals 8 and 6, so side = 10 (a 6-8-10 triangle); perimeter = 4 × 10.
Q4. The circumference of a circle is 44 cm. Find its area. (a) 77 cm² (b) 154 cm² (c) 308 cm² (d) 616 cm² Answer: (b) 154. 2πr = 44 gives r = 7; area = (22/7) × 49.
Q5. Find the area of a sector of radius 14 cm and central angle 90°. (a) 154 cm² (b) 308 cm² (c) 77 cm² (d) 616 cm² Answer: (a) 154. One quarter of (22/7) × 196 = 616.
Q6. Find the area of a regular hexagon of side 6 cm. (a) 36√3 cm² (b) 54√3 cm² (c) 72√3 cm² (d) 108 cm² Answer: (b). (3√3/2) × 36 = 54√3. A regular hexagon is six equilateral triangles.
Q7. Each interior angle of a regular polygon is 150°. How many sides does it have? (a) 10 (b) 12 (c) 15 (d) 18 Answer: (b) 12. Exterior angle = 180° − 150° = 30°; n = 360/30.
Set B: 3D Solids (Q8–Q15)
Q8. The total surface area of a cube is 216 cm². Find its volume. (a) 125 cm³ (b) 216 cm³ (c) 343 cm³ (d) 512 cm³ Answer: (b) 216. 6a² = 216 gives a = 6; a³ = 216.
Q9. Find the length of the longest rod that fits in a room 12 m × 9 m × 8 m. (a) 15 m (b) 16 m (c) 17 m (d) 19 m Answer: (c) 17. √(144 + 81 + 64) = √289.
Q10. Find the volume of a right circular cylinder of radius 7 cm and height 10 cm. (a) 440 cm³ (b) 770 cm³ (c) 1,540 cm³ (d) 3,080 cm³ Answer: (c) 1,540. (22/7) × 49 × 10. Trap: 440 is its curved surface area (2πrh).
Q11. A cone has base radius 6 cm and height 8 cm. Find its curved surface area. (a) 48π cm² (b) 60π cm² (c) 96π cm² (d) 100π cm² Answer: (b) 60π. Slant height l = √(36 + 64) = 10; CSA = π × 6 × 10.
Q12. Find the volume of a sphere of radius 21 cm. (a) 9,702 cm³ (b) 19,404 cm³ (c) 38,808 cm³ (d) 77,616 cm³ Answer: (c). (4/3) × (22/7) × 9,261 = 4 × 22 × 441 = 38,808.
Q13. Find the total surface area of a solid hemisphere of radius 7 cm. (a) 308 cm² (b) 462 cm² (c) 616 cm² (d) 924 cm² Answer: (b) 462. 3πr² = 3 × (22/7) × 49. Curved part 2πr² plus flat base πr².
Q14. A right prism has an equilateral triangle base of side 4 cm and height 10 cm. Find its volume. (a) 20√3 cm³ (b) 40√3 cm³ (c) 80 cm³ (d) 160√3 cm³ Answer: (b). Base area (√3/4) × 16 = 4√3; × 10.
Q15. A regular square pyramid has base side 10 cm and height 12 cm. Find its lateral surface area. (a) 240 cm² (b) 260 cm² (c) 340 cm² (d) 360 cm² Answer: (b) 260. Slant height = √(12² + 5²) = 13; ½ × 40 × 13. Total surface area would add the base: 260 + 100 = 360, which is option (d)'s trap.
Set C: Ratios, Change and Recasting (Q16–Q20)
Q16. If the radius of a sphere is doubled, its volume becomes how many times? (a) 2 (b) 4 (c) 6 (d) 8 Answer: (d) 8. Volume varies as r³; 2³ = 8. Surface area would become 4 times.
Q17. A cone and a cylinder have the same base radius and height. Ratio of their volumes? (a) 1 : 2 (b) 1 : 3 (c) 2 : 3 (d) 3 : 1 Answer: (b) 1 : 3. (1/3)πr²h : πr²h.
Q18. A solid metal sphere of radius 6 cm is melted and recast into a cylinder of radius 4 cm. Find the height of the cylinder. (a) 12 cm (b) 16 cm (c) 18 cm (d) 24 cm Answer: (c) 18. Volume is conserved: (4/3)π × 216 = 288π = π × 16 × h.
Q19. The length of a rectangle is increased by 20% and its breadth decreased by 20%. The area: (a) is unchanged (b) increases 4% (c) decreases 4% (d) decreases 2% Answer: (c). Net change = 20 − 20 − (20 × 20)/100 = −4%. See percentage tricks for the successive-change rule.
Q20. A 2 m wide path runs around the outside of a 40 m × 30 m garden. Find the area of the path. (a) 280 m² (b) 296 m² (c) 304 m² (d) 316 m² Answer: (b) 296. Outer rectangle 44 × 34 = 1,496; minus 1,200. Shortcut: 2w(l + b) + 4w² = 2 × 2 × 70 + 16.
Answer Key
| Q | Ans | Q | Ans | Q | Ans | Q | Ans |
|---|---|---|---|---|---|---|---|
| 1 | a | 6 | b | 11 | b | 16 | d |
| 2 | b | 7 | b | 12 | c | 17 | b |
| 3 | c | 8 | b | 13 | b | 18 | c |
| 4 | b | 9 | c | 14 | b | 19 | c |
| 5 | a | 10 | c | 15 | b | 20 | b |
Where Students Lose Marks in Mensuration
- Mixing CSA and TSA. Read whether the solid is "open" or "closed" and whether the base is counted.
- Using height instead of slant height for the curved surface of a cone or the lateral surface of a pyramid.
- Forgetting units. Areas in cm² and volumes in cm³; convert 1 m³ = 1,000 litres when tanks appear.
- Expanding π too early. Keep π as a symbol until the last step; options often contain π.
- Recasting questions: only volume is conserved, never surface area.
Practise Under Time
- Mensuration mocks: SBI PO mensuration mock test 01, RRB NTPC mensuration mock test 01
- Mixed maths: SSC CGL Tier 1 mock: Geometry and Coordinate Geometry
- Next sets: Geometry questions for SSC CGL, Trigonometry questions for SSC CGL, Algebra questions for SSC CGL
Mensuration Questions FAQs
Which mensuration topics are in the SSC CGL 2026 syllabus?
Triangle, quadrilaterals, regular polygons, circle, right prism, right circular cone and cylinder, sphere, hemispheres, rectangular parallelepiped (cuboid) and regular right pyramid with triangular or square base, in both Tier 1 and Tier 2, as per the 2026 notice.
What value of π should I use in SSC questions?
Use 22/7 unless the question gives 3.14 or leaves π in the options. Radii like 7, 14, 21 and 35 are a strong hint that 22/7 is intended.
How do I solve melting and recasting questions?
Equate volumes: volume of the original solid = total volume of the new solid(s). For n small solids, multiply the volume of one by n.
What is the difference between curved and total surface area?
Curved (lateral) surface area excludes the flat faces; total surface area adds them. For a closed cylinder TSA = 2πr(r + h); for a hemisphere TSA = 3πr².
How many mensuration questions come in SSC CGL?
SSC does not publish topic-wise counts. Mensuration is part of the Quantitative Aptitude syllabus in Tier 1 and Mathematical Abilities in Tier 2.
Practice Next for SSC Maths
- Formulas: Mensuration formulas, Coordinate geometry questions
- Plans: SSC CGL Tier 2 preparation strategy 2026, SSC CHSL preparation strategy 2026, SSC CGL syllabus 2026
Sources: SSC CGL 2026 notice (syllabus paras 13.10.3 and 13.11.1.5); SSC notice dated 01.10.2026. Questions and solutions are original BookOfExams material. Last checked 7 November 2026.