--- title: "RF and scale for 6.304 ha plot" subject: "Surveying I" chapter: 1 key: "semester_3/surveying_i:scale-plot-6-304-ha" source: https://www.bctengineer.com/q/semester_3/surveying_i/scale-plot-6-304-ha site: BCT Engineering --- # RF and scale for 6.304 ha plot Surveying I · Chapter 1: Introduction - Asked in: 2076 Chaitra, 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-6-304-ha - 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 6.304 ha is represented by 4.7 cm × 4.6 cm on the plan. Calculate the suitable RF of scale of the map and draw a scale to read upto a meter from the map; the scale should be long enough to measure upto 500 m. Also indicate 123.400 m on the scale. ## Short answer RF is about 1/5400. Scale length is 9.26 cm for 500 m, with main divisions of 1.852 cm and a left subdivision for 10 m. Diagonal steps read 1 m; mark 123.4 m using the 100 vertical, 20 diagonal, and a point 0.4 between the 3rd and 4th horizontal lines. ## Answer #### RF Ground area $= 6.304$ ha $= 6.304 \times 10^{4}$ m$^2 = 6.304 \times 10^{8}$ cm$^2$. Map area $= 4.7 \times 4.6 = 21.62$ cm$^2$. $$ \text{RF}^2 = \frac{21.62}{6.304 \times 10^{8}} = 3.4296 \times 10^{-8} $$ $$ \text{RF} = 1.852 \times 10^{-4} \approx \frac{1}{5400} $$ #### Scale length (to read 1 m, up to 500 m) $$ \frac{500 \times 100}{5400} = 9.26\ \text{cm} $$ 100 m $= 1.852$ cm, 10 m $= 0.1852$ cm, 1 m $= 0.01852$ cm. #### Construction (diagonal scale) 1. Draw a line 9.26 cm long and divide it into 5 main divisions of 1.852 cm (100 m each), numbered 0, 100, ... 500. Extend one more division of 1.852 cm to the left of 0. 2. Divide this left division into 10 parts (10 m each, 0.1852 cm). 3. Draw 10 horizontal lines at equal spacing and the diagonals from the top of each sub-division to the next lower sub-division on the base. Each step along a diagonal reads 1 m. #### Indicating 123.400 m $123.4 = 100 + 20 + 3 + 0.4$. Take the vertical at 100 and the diagonal from the 20 sub-division. On this diagonal, mark a point 0.4 of the way from the 3rd to the 4th horizontal line (estimated by eye, since 0.4 m is only about 0.007 cm on the map). The horizontal distance from this point to the vertical at 100 represents 123.4 m. ```text 10 | / / / / / / / / / / | 3 | .. 123.4 m | 0 +---+---+---+---+---+---+---------+ 90..0 100 200 300 400 500 (m) ``` **Answer: RF = 1/5400; scale length = 9.26 cm (plus the left sub-divided part).** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. 6.304 ha in cm^2 is A. 6.304 x 10^4 cm^2 B. 6.304 x 10^8 cm^2 C. 6.304 x 10^6 cm^2 D. 6.304 x 10^10 cm^2 Answer: B. 1 ha = 10^4 m^2 = 10^8 cm^2. (Key point: Unit conversion) 2. The RF obtained is about A. 1/5400 B. 1/540 C. 1/3400 D. 1/54,000 Answer: A. RF = sqrt(21.62 / 6.304 x 10^8) = 1.852 x 10^-4. (Key point: RF) 3. Scale length for 500 m is about A. 5 cm B. 18.5 cm C. 9.26 cm D. 0.926 cm Answer: C. 500 x 100 / 5400 = 9.26 cm. (Key point: Length) 4. 123.400 m is marked using A. 123 + 0.4 only on the plain scale B. vertical at 120 with 4th line C. 100 + 2 + 34 D. 100 + 20 + 3 and an estimated 0.4 m above the 3rd line Answer: D. The 0.4 m is estimated by eye beyond the third line. (Key point: 123.4 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 51750 m² plot](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ascale-plot-51750-sqm) — 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× - [Scale and area on topo sheet](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ascale-plot-18000-sqm) — Surveying I, chapter 1 ## Related in other subjects - [Flying height from photo and map scale](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aflying-height-pq-20cm-focal-24) — Surveying II, chapter 7