---
title: "Scale for 1.5 km road on map"
subject: "Surveying I"
chapter: 1
key: "semester_3/surveying_i:scale-road-1-5-km"
source: https://www.bctengineer.com/q/semester_3/surveying_i/scale-road-1-5-km
site: BCT Engineering
---

# Scale for 1.5 km road on map

Surveying I · Chapter 1: Introduction

- Asked in: 2076 Asoj, 4 marks
- Video: [Scale of a map - map distance : actual distance | SHS 1 CORE MATH](https://www.youtube.com/watch?v=_wMl_-vyRIE) — SkanCity Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/scale-road-1-5-km
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-1

## Question

A 1.5 km long road is indicated in a map by a length of 37.5 cm. Find the scale of the plot and indicate through a sketch how a suitable scale can be constructed to read upto 1 m in the map.

## Short answer

RF is 1/4000, so 1 cm equals 40 m. A diagonal scale 12.5 cm long reads 1 m up to 500 m; divide into five 100 m parts of 2.5 cm, subdivide left part into 10 m, and draw diagonals for 1 m steps.

## Answer

#### Scale (RF)
1.5 km $= 1500$ m $= 1.5 \times 10^{5}$ cm is shown by 37.5 cm.

$$
\text{RF} = \frac{37.5}{1.5 \times 10^{5}} = \frac{1}{4000}
$$

so 1 cm on the map $= 40$ m on the ground.

#### Scale to read 1 m
A diagonal scale is suitable. Take a maximum reading of 500 m.

$$
\text{Length} = \frac{500 \times 100}{4000} = 12.5\ \text{cm}
$$

100 m $= 2.5$ cm, 10 m $= 0.25$ cm, 1 m $= 0.025$ cm.

#### Sketch and construction
1. Draw a line 12.5 cm long; divide it into 5 equal parts of 2.5 cm (100 m). Extend by one more division to the left of 0.
2. Divide the left division into 10 equal parts (10 m each).
3. Draw 10 horizontal lines through equal divisions of a vertical 2.5 cm high.
4. Join the top of each sub-division with the next lower sub-division at the base (diagonals). Each horizontal line cuts a diagonal at 1 m steps.

```text
 10 |  /  /  /  /  /  /  /  /  /  /  |
  5 | /  /                            |
  0 +---+----+----+----+----+----+----+
   90..0  100  200  300  400  500 (m)
```
Example: 234 m is 200 m + 30 m + 4 m.

**Answer: RF = 1/4000 (1 cm = 40 m); diagonal scale length 12.5 cm.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. 1.5 km shown by 37.5 cm gives RF
   A. 1/400
   B. 1/40,000
   C. 1/4000
   D. 1/1500
   Answer: C. 37.5 / 1.5 x 10^5 = 1/4000. (Key point: RF)

2. With this RF, 1 cm on the map equals
   A. 40 m
   B. 4 m
   C. 400 m
   D. 4000 m
   Answer: A. 4000 cm = 40 m. (Key point: 1 cm)

3. To read up to 1 m a suitable scale is
   A. a plain scale
   B. a diagonal scale
   C. a scale of chords
   D. a time scale
   Answer: B. A diagonal scale reads three units. (Key point: Scale type)

4. A diagonal scale for 500 m is
   A. 5 cm long
   B. 25 cm long
   C. 1.25 cm long
   D. 12.5 cm long
   Answer: D. 500 x 100 / 4000 = 12.5 cm. (Key point: Length)

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