---
title: "RF and scale for 51072 m² plot"
subject: "Surveying I"
chapter: 1
key: "semester_3/surveying_i:scale-plot-51072-sqm"
source: https://www.bctengineer.com/q/semester_3/surveying_i/scale-plot-51072-sqm
site: BCT Engineering
---

# RF and scale for 51072 m² plot

Surveying I · Chapter 1: Introduction

- Asked in: 2080 Baisakh, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/scale-plot-51072-sqm
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-1

## Question

A map is drawn to some scale so that a plot of 51072 m² is represented by 4.56 cm × 4.48 cm on the plan. Calculate the suitable RF of scale of the map and draw a scale to read upto a metre from the map; the scale should be long enough to measure upto 600 m.

## Short answer

RF is 1/5000. A diagonal scale of length 12 cm is needed to read 1 m up to 600 m, with 100 m divisions of 2 cm and 10 m subdivisions. It is constructed with 10 horizontal lines and diagonals giving 1 m steps.

## Answer

#### RF from the area
Area on map $= 4.56 \times 4.48 = 20.4288$ cm$^2$. Ground area $= 51072$ m$^2$ $= 51072 \times 10^{4}$ cm$^2 = 5.1072 \times 10^{8}$ cm$^2$.

$$
\text{RF}^2 = \frac{20.4288}{5.1072 \times 10^{8}} = 4.0 \times 10^{-8}
$$

$$
\text{RF} = 2 \times 10^{-4} = \frac{1}{5000}
$$

#### Scale
Length for 600 m $= \dfrac{600 \times 100}{5000} = 12$ cm. Here 100 m $= 2$ cm, 10 m $= 0.2$ cm and 1 m $= 0.02$ cm. Since 1 m is only 0.2 mm on the map, a **diagonal scale** is needed.

#### Construction
1. Draw a 12 cm line and divide it into 6 main divisions of 2 cm (100 m each). Mark 0 at the end of the first (left) division and number the others 100, 200, ... 500.
2. Divide the left division into 10 parts of 0.2 cm (10 m each).
3. Draw 10 equally spaced horizontal lines (total height, say, 2 cm), erect perpendiculars at each main division, and draw diagonals from the top of each sub-division to the next lower sub-division on the base. The steps along the diagonals read 1 m.

```text
 10 |  /  /  /  /  /  /  /  /  /  /  |
  5 | /  /                            |
  0 +---+---+---+---+---+---+---+---+-+
   90..0  100  200  300  400  500 (m)
```

**Answer: RF = 1/5000; diagonal scale length = 12 cm, reading 1 m up to 600 m.**

## Check yourself

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

1. RF is found from areas using
   A. RF = map area / ground area
   B. RF^2 = map area / ground area
   C. RF = ground area / map area
   D. RF^2 = ground length
   Answer: B. Areas scale as the square of the linear scale. (Key point: Area method)

2. For 51072 m^2 shown by 4.56 x 4.48 cm, RF is
   A. 1/5000
   B. 1/500
   C. 1/2500
   D. 1/50,000
   Answer: A. RF^2 = 20.4288 / 5.1072 x 10^8 = 4 x 10^-8, RF = 2 x 10^-4. (Key point: RF value)

3. Length for 600 m is
   A. 6 cm
   B. 24 cm
   C. 12 cm
   D. 1.2 cm
   Answer: C. 600 x 100 / 5000 = 12 cm. (Key point: Length)

4. Why is a diagonal scale needed here?
   A. Because the area is large
   B. Because RF is too large
   C. Because 600 m is too short
   D. 1 m is only 0.2 mm on the map, too small for a plain scale
   Answer: D. 1 m = 0.02 cm. (Key point: Scale type)

## Close variants set in other exams

- [RF and scale for 51750 m² plot](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ascale-plot-51750-sqm) — Surveying I, chapter 1, asked 3×
- [RF and scale for 6.304 ha plot](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ascale-plot-6-304-ha) — Surveying I, chapter 1, asked 3×

## Related in Surveying I

- [RF and scale for 0.55 hectare plot](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ascale-plot-0-55-hectare) — Surveying I, chapter 1
- [Scale for 39672 m² plan](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ascale-plot-39672-sqm) — Surveying I, chapter 1
- [Diagonal scale: hydropower dam-powerhouse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Adiagonal-scale-hydropower-1m) — Surveying I, chapter 1
- [Scale for 1.5 km road on map](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ascale-road-1-5-km) — Surveying I, chapter 1
- [Diagonal scale: Kathmandu-Pokhara highway map](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Adiagonal-scale-kathmandu-pokhara-224) — Surveying I, chapter 1, asked 2×