Mensuration (RRB)
2D: triangle, rectangle, circle. 3D: cube, cuboid, cylinder, cone, sphere.
Mensuration (RRB) — Core
2D: triangle, rectangle, circle. 3D: cube, cuboid, cylinder, cone, sphere.
Mensuration formulas — RRB reference
Notes
2D — Area & Perimeter:
- Square: A = a²; P = 4a; diagonal = a√2.
- Rectangle: A = lb; P = 2(l+b); diagonal = √(l²+b²).
- Triangle: A = ½ × base × height. Heron: √(s(s−a)(s−b)(s−c)).
- Equilateral triangle: A = √3/4 × side²; height = √3/2 × side.
- Circle: A = πr²; C = 2πr.
- Sector: A = (θ/360)·πr²; arc = (θ/360)·2πr.
- Rhombus: A = ½ × d1 × d2.
- Trapezium: A = ½ × (sum of parallel sides) × height.
3D — Volume & Surface Area:
| Shape | LSA | TSA | Volume |
|---|---|---|---|
| Cube (a) | 4a² | 6a² | a³ |
| Cuboid (l,b,h) | 2h(l+b) | 2(lb+bh+hl) | lbh |
| Cylinder (r,h) | 2πrh | 2πr(r+h) | πr²h |
| Cone (r,h,l) | πrl | πr(r+l) | (1/3)πr²h |
| Sphere (r) | — | 4πr² | (4/3)πr³ |
| Hemisphere (r) | 2πr² | 3πr² | (2/3)πr³ |
Cone slant: l = √(r² + h²).
π = 22/7 if r is multiple of 7.