Mensuration Cheat Sheet
31 Oct 2026
Quick answer
A quick revision cheat sheet on mensuration for SSC, Banking, Railway and state exams. It gathers the area and perimeter formulas for the common 2D shapes and the volume and surface-area formulas for the common 3D solids — cube, cuboid, cylinder, cone, sphere and hemisphere — in one place for fast revision.
Mensuration Cheat Sheet
Quick Revision
Mensuration is the measurement of shapes: the area and perimeter of flat (2D) figures, and the volume and surface area of solid (3D) figures. Use π = 22/7 or 3.14 as the question states.
Ready to practise? Take the Mensuration quiz
1. 2D Shapes — Area and Perimeter
| Shape | Area | Perimeter |
|---|---|---|
| Square | a² | 4a (diagonal a√2) |
| Rectangle | l × b | 2(l + b) (diagonal √(l²+b²)) |
| Triangle | ½ × base × height | a + b + c |
| Equilateral triangle | (√3 / 4) × a² | 3a |
| Parallelogram | base × height | 2(sum of adjacent sides) |
| Rhombus | ½ × d₁ × d₂ | 4 × side |
| Trapezium | ½ × (sum of parallel sides) × height | sum of all sides |
| Circle | πr² | 2πr (circumference) |
Heron's formula (triangle with sides a, b, c): Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2.
2. 3D Solids — Volume and Surface Area
| Solid | Volume | Curved / Lateral SA | Total SA |
|---|---|---|---|
| Cube | a³ | 4a² | 6a² |
| Cuboid | l × b × h | 2h(l + b) | 2(lb + bh + hl) |
| Cylinder | πr²h | 2πrh | 2πr(r + h) |
| Cone | ⅓ πr²h | πrl | πr(r + l) |
| Sphere | (4/3) πr³ | — | 4πr² |
| Hemisphere | (2/3) πr³ | 2πr² | 3πr² |
Cone slant height: l = √(r² + h²). Cube diagonal: a√3. Cuboid diagonal: √(l² + b² + h²).
3. Worked Example
A cylinder has radius 7 cm and height 10 cm (π = 22/7).
Volume = πr²h = (22/7) × 7 × 7 × 10 = 1540 cm³
CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm²4. Exam Quick Tips
- Note which π the question wants — 22/7 for multiples of 7, else 3.14.
- Keep units consistent; convert before you compute.
- For a cone, find the slant height
l = √(r²+h²)before the curved surface area. - Learn the sphere set: volume
(4/3)πr³, surface area4πr².
Keep revising with the rest of the Maths section:
How this was made: Drafted with AI assistance; spot-checked by the editor on 31 October 2026.