--- title: "RF and scale for 0.55 hectare plot" subject: "Surveying I" chapter: 1 key: "semester_3/surveying_i:scale-plot-0-55-hectare" source: https://www.bctengineer.com/q/semester_3/surveying_i/scale-plot-0-55-hectare site: BCT Engineering --- # RF and scale for 0.55 hectare plot Surveying I · Chapter 1: Introduction - Asked in: 2074 Chaitra, 4 marks - Video: [#A rectarngular plot/RGPV 2023 QUESTIONS/0.45 HECTARE/#5 SUARE METER/#CALCULATE THE RF/#DRAW A SCALE](https://www.youtube.com/watch?v=BOVtKg3Atd8) — TECHNICAL PRABHAT ZONE(ENGG.DRAWING+B-TECH,DIPLOMA - 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-0-55-hectare - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-1 ## Question A rectangular plot of land of area 0.55 hectare is represented on a map of similar rectangle area of 6.11 cm². Calculate the representative factor of the scale of the map. Draw a scale to read upto a meter from the map. The scale should be long enough to measure upto 400 m. ## Short answer RF = 1/3000. A diagonal scale 13.33 cm long represents 400 m and reads single metres. ## Answer #### RF Ground area $= 0.55$ ha $= 5500$ m$^2 = 5500 \times 10^{4}$ cm$^2 = 5.5 \times 10^{7}$ cm$^2$. Map area $= 6.11$ cm$^2$. $$ \text{RF}^2 = \frac{6.11}{5.5 \times 10^{7}} = 1.1109 \times 10^{-7} $$ $$ \text{RF} = 3.3331 \times 10^{-4} \approx \frac{1}{3000} $$ #### Scale (to read 1 m, up to 400 m) $$ \text{Length} = \frac{400 \times 100}{3000} = 13.33\ \text{cm} $$ 100 m $= 3.333$ cm, 10 m $= 0.3333$ cm, 1 m $= 0.0333$ cm: a diagonal scale. #### Construction 1. Draw a 13.33 cm line with 4 main divisions of 3.333 cm (100 m). Add one division to the left of 0. 2. Divide the left division into 10 parts (10 m each). 3. Draw 10 equally spaced horizontal lines on a rectangle 3 cm high. 4. Draw the diagonals from the top of each sub-division to the next lower sub-division on the base. Each diagonal step gives 1 m. ```text 10 | / / / / / / / / / / | 5 | / / | 0 +---+----+----+----+--------------+ 90..0 100 200 300 400 (m) ``` **Answer: RF = 1/3000; scale length = 13.33 cm.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is 0.55 hectare in cm^2? A. 5.5 x 10^3 B. 5.5 x 10^5 C. 5.5 x 10^7 D. 5.5 x 10^9 Answer: C. 0.55 ha = 5500 m^2 = 5500 x 10^4 cm^2 = 5.5 x 10^7 cm^2. (Key point: Hectare conversion) 2. RF^2 = 6.11 / (5.5 x 10^7) = 1.11 x 10^-7. What does the RF come to (rounded)? A. 1/3000 B. 1/9000 C. 1/300 D. 1/30000 Answer: A. RF = sqrt(1.11 x 10^-7) = 3.33 x 10^-4, about 1/3000. (Key point: RF from areas) 3. What is the length of the scale to measure 400 m at RF 1/3000? A. 4 cm B. 13.33 cm C. 1.33 cm D. 40 cm Answer: B. 400 x 100 / 3000 = 13.33 cm. (Key point: Scale length) 4. How long is each 100 m main division on this scale? A. 3.333 cm B. 0.333 cm C. 33.3 cm D. 1 cm Answer: A. 100 m x 100 / 3000 = 3.333 cm. (Key point: Main division) ## Related in Surveying I - [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× - [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× - [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 - [Scale for 39672 m² plan](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ascale-plot-39672-sqm) — Surveying I, chapter 1 ## Related in other subjects - [Channel earthwork and land area, 50 cm fall](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-land-acquisition-h) — Estimating and Costing, chapter 6, asked 2× - [Channel earthwork and land area, bed 4 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-land-acquisition-f) — Estimating and Costing, chapter 6, asked 2× - [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