--- title: "Diagonal scale: Pokhara-Kathmandu 200 km" subject: "Surveying I" chapter: 1 key: "semester_3/surveying_i:diagonal-scale-pokhara-kathmandu-222" source: https://www.bctengineer.com/q/semester_3/surveying_i/diagonal-scale-pokhara-kathmandu-222 site: BCT Engineering --- # Diagonal scale: Pokhara-Kathmandu 200 km Surveying I · Chapter 1: Introduction - Asked in: 2081 Baisakh, 2+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/diagonal-scale-pokhara-kathmandu-222 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-1 ## Question The distance between Pokhara and Kathmandu is 200 km. In a map, it is represented by a line 5 cm long. Find its RF. Draw a diagonal scale to show single km and maximum 600 km. Indicate on it the following distances: (i) 222 km (ii) 336 km. ## Short answer RF is 1/4,000,000 and scale length is 15 cm. Draw 6 main divisions of 2.5 cm for 100 km each, subdivide left part into 10 km, and add diagonals for 1 km steps. Mark 222 km using 200 + 20 + 2 and 336 km using 300 + 30 + 6. ## Answer #### RF Ground distance = 200 km $= 200 \times 10^5$ cm $= 2 \times 10^7$ cm; map distance = 5 cm. $$ \text{RF} = \frac{5}{2 \times 10^7} = \frac{1}{4{,}000{,}000} $$ #### Length of the diagonal scale $$ \text{Length} = \frac{600\ \text{km} \times 10^5\ \text{cm}}{4 \times 10^6} = 15\ \text{cm} $$ 1 km on the scale $= 10^5/(4\times10^6) = 0.025$ cm; 10 km $= 0.25$ cm; 100 km $= 2.5$ cm. #### Construction 1. Draw a line 15 cm long and divide it into 6 equal parts of 2.5 cm; each represents 100 km. Number them 0, 100, ... 500 starting from the end of the first division (the first, left-hand division is the one that is sub-divided). 2. Divide the left-most main division into 10 equal parts of 0.25 cm; each is 10 km. Number them 10, 20, ... 90 to the left of 0. 3. At the ends, erect perpendiculars of height 2.5 cm (any convenient height) and divide each into 10 equal parts; draw horizontal lines through these points. Complete the rectangle. 4. Join the top of the first sub-division (10 km) to the 0 on the bottom line, and draw diagonals parallel to it through each of the other sub-divisions. Each horizontal step along a diagonal is 1 km (0.025 cm). ```text 10 | / / / / / / / / / /| 8 | / / / | 6 | / / | 4 | / / | 2 |/ | 0 +---+---+---+---+---+---+---+---+---+ 90..10 0 100 200 300 400 500 (km) ``` #### Indicating the distances - **(i) 222 km** $= 200 + 20 + 2$: take the vertical line at 200, the diagonal that starts at the 20 km sub-division, and the 2nd horizontal line. Mark the point where this diagonal meets the 2nd horizontal line; the length along that line from this point to the vertical at 200 is 222 km. - **(ii) 336 km** $= 300 + 30 + 6$: use the vertical at 300, the diagonal from the 30 km sub-division and the 6th horizontal line. **Answer: RF = 1/4,000,000; scale length = 15 cm.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. 200 km is shown by 5 cm. The RF is A. 1/4,000,000 B. 1/400,000 C. 1/2,000,000 D. 1/40,000 Answer: A. 5/(2 x 10^7) = 1/4,000,000. (Key point: RF) 2. Length of the scale for 600 km is A. 6 cm B. 30 cm C. 15 cm D. 150 cm Answer: C. 600 x 10^5 / (4 x 10^6) = 15 cm. (Key point: Length) 3. Each main division of 100 km is A. 0.25 cm B. 2.5 cm C. 5 cm D. 0.025 cm Answer: B. 100 km = 10^7 cm / (4 x 10^6) = 2.5 cm. (Key point: Main division) 4. To mark 222 km, use the vertical at 200, the diagonal from A. 2 km and the 20th line B. 22 km and the 2nd line C. 10 km and the 22nd line D. 20 km sub-division and the 2nd horizontal line Answer: D. 222 = 200 + 20 + 2. (Key point: 222 km) ## Close variants set in other exams - [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× ## Related in Surveying I - [Diagonal scale: BP highway 158 km](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Adiagonal-scale-bp-highway) — 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 - [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× - [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×