--- title: "Diagonal scale: Kathmandu-Pokhara highway map" subject: "Surveying I" chapter: 1 key: "semester_3/surveying_i:diagonal-scale-kathmandu-pokhara-224" source: https://www.bctengineer.com/q/semester_3/surveying_i/diagonal-scale-kathmandu-pokhara-224 site: BCT Engineering --- # Diagonal scale: Kathmandu-Pokhara highway map Surveying I · Chapter 1: Introduction - Asked in: 2078 Bhadra, 5 marks - Video: [Diagonal Scale Example 5 | MechGate](https://www.youtube.com/watch?v=0nq3NIpAwWk) — MechGate - 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-kathmandu-pokhara-224 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-1 ## Question The distance between Kathmandu and Pokhara is 200 km. In a highway map it is represented by a line 5 cm long. Find its R.F. Draw a diagonal scale to show single km and maximum 600 km. Indicate the following distances: a) 224 km b) 338 km c) 459 km d) 579 km. ## Short answer RF is 1/4,000,000 and scale length is 15 cm. Use six 100 km divisions of 2.5 cm, subdivide left part into 10 km, and add diagonals for 1 km. Mark 224 as 200+20+4, 338 as 300+30+8, 459 as 400+50+9, and 579 as 500+70+9. ## Answer #### RF 200 km $= 2 \times 10^7$ cm is shown by 5 cm. $$ \text{RF} = \frac{5}{2 \times 10^{7}} = \frac{1}{4{,}000{,}000} $$ #### Scale length $$ \frac{600 \times 10^{5}}{4 \times 10^{6}} = 15\ \text{cm} $$ So 100 km $= 2.5$ cm, 10 km $= 0.25$ cm and 1 km $= 0.025$ cm. #### Construction 1. Draw a 15 cm line and divide it into 6 main divisions of 2.5 cm (100 km). Mark 0 at the end of the first division and 100, 200 ... 500 for the others. 2. Divide the first main division into 10 parts of 0.25 cm (10 km each). 3. On the end verticals mark 10 equal divisions (height 2.5 cm) and draw 10 horizontal lines. 4. Draw the diagonals from the top of each sub-division to the next lower sub-division on the base line. A step on the diagonal between two horizontal lines is 1 km. ```text 10 | / / / / / / / / / / | 5 | / / | 0 +---+---+---+---+---+---+---+---+-+ 90..0 100 200 300 400 500 (km) ``` #### Distances | Distance | Split | Vertical | Diagonal from | Horizontal line | |---|---|---|---|---| | (a) 224 km | 200 + 20 + 4 | 200 | 20 | 4th | | (b) 338 km | 300 + 30 + 8 | 300 | 30 | 8th | | (c) 459 km | 400 + 50 + 9 | 400 | 50 | 9th | | (d) 579 km | 500 + 70 + 9 | 500 | 70 | 9th | The required length is measured between the vertical line and the point where the diagonal meets the 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. The RF of the highway map is A. 1/400,000 B. 1/4,000,000 C. 1/2,000,000 D. 1/224 Answer: B. 5/(2 x 10^7). (Key point: RF) 2. The scale length for 600 km is A. 15 cm B. 12 cm C. 30 cm D. 6 cm Answer: A. 600 km x 10^5 / 4 x 10^6 = 15 cm. (Key point: Length) 3. 579 km is split as A. 500 + 7 + 9 B. 570 + 9 + 0 C. 500 + 70 + 9, using the diagonal from 70 D. 579 + 0 + 0 Answer: C. Hundreds, tens, units. (Key point: 579 km) 4. A step on a diagonal between two adjacent horizontal lines represents A. 10 km B. 100 km C. 0.1 km D. 1 km Answer: D. Each tenth of a 10 km sub-division is 1 km. (Key point: Diagonal step) ## Close variants set in other exams - [Diagonal scale: Pokhara-Kathmandu 200 km](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Adiagonal-scale-pokhara-kathmandu-222) — 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