Mensuration — RRB NTPC Mathematics
This topic carries roughly 9% of Mathematics's 30 questions. Nearly every question is a direct formula application — the preparation here is almost entirely about having the formula table memorised correctly and matching the right shape to the right question.
1. What RRB NTPC actually asks
Expect direct area/perimeter calculations for rectangles, squares, triangles, circles, and trapeziums; surface area and volume calculations for cubes, cuboids, and cylinders; and applied word problems (a path around a field, a room requiring flooring).
2. 2-D formulas
| Shape | Area | Perimeter |
|---|---|---|
| Rectangle | length × breadth | 2(length + breadth) |
| Square | side² | 4 × side |
| Triangle | ½ × base × height | sum of three sides |
| Circle | πr² | 2πr |
| Trapezium | ½ × (sum of parallel sides) × height | sum of all four sides |
Use π ≈ 22/7 when the radius is a multiple of 7 (for a clean answer without a calculator), and π ≈ 3.14 otherwise.
3. 3-D formulas
| Shape | Volume | Total surface area |
|---|---|---|
| Cube | side³ | 6 × side² |
| Cuboid | length × breadth × height | 2(lb + bh + hl) |
| Cylinder | πr²h | 2πr(r + h) |
Curved surface area of a cylinder (excluding the two circular ends) is 2πrh — used when only the lateral surface matters (e.g., wrapping a label around a can).
4. Applied word problems: paths around a field
For a rectangular field with a path of uniform width w built around the outside, the path area = (outer rectangle's area) − (inner/original rectangle's area), where the outer rectangle's dimensions are (length + 2w) × (breadth + 2w).
Worked examples
Q1. What is the area of a circle with radius 7 cm? (Use π = 22/7)
Pick an option to check your answer.
Show explanation
Solution. Area = πr² = (22/7) × 7² = (22/7) × 49 = 22 × 7 = 154 cm².
Choosing radius 7 specifically lets 22/7 cancel cleanly against 49 — this is why exam questions often use multiples of 7 for the radius. Answer: (b).
Q2. A rectangular field is 60 m long and 40 m wide. A path 2 m wide is built around the outside of the field. What is the area of the path?
Pick an option to check your answer.
Show explanation
Solution. The outer rectangle (field + path on all sides) measures (60+2×2) × (40+2×2) = 64 × 44 = 2,816 m². The inner (original field) area = 60 × 40 = 2,400 m².
Path area = 2,816 − 2,400 = 416 m². A common error is adding only one width (2m, not 4m) to each dimension, forgetting the path runs on both sides. Answer: (c).
6. Common traps
- Adding the path width once instead of twice to each dimension when the path runs around all four sides — it adds to both ends of the length and both ends of the breadth.
- Confusing curved surface area with total surface area of a cylinder. CSA = 2πrh (lateral only); TSA = 2πr(r+h) (lateral plus both circular ends).
- Using π = 22/7 when the radius isn't a multiple of 7, producing an answer that doesn't match any clean option — use 3.14 in that case instead, or check if the 22/7 form simplifies anyway.
- Confusing area formulas across shapes, especially triangle (½ × base × height) versus parallelogram (base × height, no half) — these are easy to mix up under time pressure.
7. Guessing strategy
A quick order-of-magnitude estimate (roughly how big should this area or volume be?) is often enough to eliminate at least one clearly-wrong-magnitude option, especially in multi-step word problems.
Summary
- Mensuration is roughly 9% of Mathematics's 30 CBT 1 questions — almost entirely a formula-recall topic.
- Memorise area/perimeter formulas for rectangle, square, triangle, circle, and trapezium, and volume/surface-area formulas for cube, cuboid, and cylinder.
- Use π = 22/7 when the radius is a multiple of 7 for a clean answer; use 3.14 otherwise.
- Curved surface area (lateral only) and total surface area (including ends) of a cylinder are different formulas — don't confuse them.
- For a path around a rectangular field, add the path width to BOTH sides of each dimension before computing the outer area.
- A quick order-of-magnitude sanity check often eliminates a wrong option fast.
