Mensuration – Railway RRB (Mathematics)
Mensuration is the branch of mathematics that deals with the area, volume, and surface area of geometric figures.
It is a compulsory part of the Railway RRB (Recruitment Board) exam and is often tested with quick‑fire MCQs and applied‑problem questions.
1. Simple Explanation
| Term | What it means | Typical use in Railway RRB |
|---|---|---|
| Area | The amount of two–dimensional space occupied by a figure. | Finding floor space of a station, track width, etc. |
| Perimeter | The total length of the boundary of a 2‑D shape. | Calculating track length, fencing, etc. |
| Volume | The amount of 3‑D space inside a solid. | Capacity of tanks, storage silos, etc. |
| Surface Area | Total area of all exposed surfaces of a solid. | Paint or coating required for a rail car. |
Units – Use
m²,km²for area;m,kmfor perimeter;m³,km³for volume.
2. Key Points & Formulae
Notation
( r ) – radius, ( R ) – outer radius, ( h ) – height, ( L ) – length, ( W ) – width, ( B ) – base, ( V ) – volume, ( A ) – area, ( SA ) – surface area.
2.1 2‑D Figures
| Figure | Area Formula | Perimeter Formula | Notes |
|---|---|---|---|
| Rectangle | (A = L \times W) | (P = 2(L+W)) | |
| Square | (A = a^2) | (P = 4a) | |
| Triangle | (A = \frac{1}{2} \times \text{base} \times \text{height}) | (P = a + b + c) | For right triangle: (A = \frac{1}{2}ab) |
| Circle | (A = \pi r^2) | (P = 2\pi r) | |
| Parallelogram | (A = \text{base} \times \text{height}) | (P = 2(\text{base} + \text{side})) | |
| Trapezium | (A = \frac{1}{2}(\text{top}+ \text{bottom})\times \text{height}) | (P = a+b+c+d) |
2.2 3‑D Figures
| Figure | Volume Formula | Surface Area (lateral + bases) | Notes |
|---|---|---|---|
| Cube | (V = a^3) | (SA = 6a^2) | |
| Cuboid | (V = LWH) | (SA = 2(LW + LH + WH)) | |
| Sphere | (V = \frac{4}{3}\pi r^3) | (SA = 4\pi r^2) | |
| Cylinder | (V = \pi r^2 h) | (SA = 2\pi r h + 2\pi r^2) | |
| Cone | (V = \frac{1}{3}\pi r^2 h) | (SA = \pi r l + \pi r^2) | (l = \sqrt{r^2+h^2}) (slant height) |
| Right Circular Conical Frustum | (V = \frac{1}{3}\pi h (r_1^2 + r_1 r_2 + r_2^2)) | (SA = \pi (r_1 + r_2) l + \pi r_1^2 + \pi r_2^2) | |
| Pyramid | (V = \frac{1}{3} B h) | (SA = B + \frac{1}{2}p \times l) | (B) – base area, (p) – perimeter of base, (l) – slant height |
| Frustum of a Pyramid | (V = \frac{h}{3}(B_1 + B_2 + \sqrt{B_1 B_2})) | (SA = B_1 + B_2 + \frac{1}{2}p \times l) |
Common Shortcuts
| Question type | Shortcut |
|---|---|
| Area of triangle with side lengths given (Heron’s formula) | (A = \sqrt{s(s-a)(s-b)(s-c)}), (s = \frac{a+b+c}{2}) |
| Area of a circle given diameter (d) | (A = \frac{\pi d^2}{4}) |
| Volume of a cylinder given diameter (D) | (V = \frac{\pi D^2 h}{4}) |
| Surface area of a cone given slant height (l) | (SA = \pi r(l+r)) |
2.3 Quick RRB Tips
- Always convert units to the same system (e.g., meters) before calculations.
- Keep (\pi = 3.14) for quick mental estimation unless higher precision is required.
- Use “slant height” (l = \sqrt{r^2 + h^2}\