---
title: "RF and scale for 51750 m² plot"
subject: "Surveying I"
chapter: 1
key: "semester_3/surveying_i:scale-plot-51750-sqm"
source: https://www.bctengineer.com/q/semester_3/surveying_i/scale-plot-51750-sqm
site: BCT Engineering
---

# RF and scale for 51750 m² plot

Surveying I · Chapter 1: Introduction

- Asked in: 2075 Asoj, 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-51750-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 51750 m² is represented by 4.6 cm × 4.5 cm on the plan. Calculate the RF of the scale of the map. Draw a scale to read up to a single metre from the map; the scale should be long enough to measure upto 600 m.

## Short answer

RF = 1/5000. A diagonal scale 12 cm long represents 600 m and can read single metres.

## Answer

#### RF
Map area $= 4.6 \times 4.5 = 20.7$ cm$^2$. Ground area $= 51750 \times 10^{4} = 5.175 \times 10^{8}$ cm$^2$.

$$
\text{RF}^2 = \frac{20.7}{5.175 \times 10^{8}} = 4.0 \times 10^{-8}, \qquad \text{RF} = 2 \times 10^{-4} = \frac{1}{5000}
$$

#### Scale (to read 1 m, up to 600 m)
$$
\text{Length} = \frac{600 \times 100}{5000} = 12\ \text{cm}
$$

100 m $= 2$ cm, 10 m $= 0.2$ cm, 1 m $= 0.02$ cm: a diagonal scale is needed.

#### Construction
1. Draw a 12 cm line and divide it into 6 main divisions of 2 cm (100 m). Add one more division to the left of 0 and mark 0, 100 ... 600.
2. Divide the left division into 10 parts (10 m each).
3. Draw 10 equal horizontal lines on a rectangle (height about 2 cm).
4. Draw diagonals joining the top of each sub-division with the next lower sub-division on the base. A diagonal step is 1 m.

```text
 10 |  /  /  /  /  /  /  /  /  /  /  |
  5 | /  /                            |
  0 +---+----+----+----+----+----+----+
   90..0  100  200  300  400  500  600
```

**Answer: RF = 1/5000; scale length = 12 cm.**

## Check yourself

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

1. Map area 20.7 cm^2 and ground area 5.175 x 10^8 cm^2 give RF^2 = 4 x 10^-8. What is the RF?
   A. 1/2500
   B. 1/5000
   C. 1/25000
   D. 1/50000
   Answer: B. RF = sqrt(4 x 10^-8) = 2 x 10^-4 = 1/5000. (Key point: RF from areas)

2. What length of line represents 600 m at RF 1/5000?
   A. 12 cm
   B. 6 cm
   C. 30 cm
   D. 120 cm
   Answer: A. 600 x 100 / 5000 = 12 cm, i.e. 2 cm per 100 m. (Key point: Scale length)

3. In the construction, how is the extra division left of 0 used?
   A. Divided into 6 parts of 100 m
   B. Divided into 10 parts of 10 m each, which the diagonals then split into 1 m
   C. Left blank as a margin
   D. Divided into 100 parts of 1 m
   Answer: B. The left division (100 m) is divided into 10 parts of 10 m, and the diagonals give the 1 m steps. (Key point: Construction of sub-divisions)

4. What does each step along a diagonal represent?
   A. 10 m
   B. 0.1 m
   C. 100 m
   D. 1 m
   Answer: D. Ten horizontal lines with diagonals divide each 10 m sub-division into ten 1 m steps. (Key point: Reading 1 m)

## Close variants set in other exams

- [RF and scale for 51072 m² plot](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ascale-plot-51072-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×

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