--- title: "Scale for 39672 m² plan" subject: "Surveying I" chapter: 1 key: "semester_3/surveying_i:scale-plot-39672-sqm" source: https://www.bctengineer.com/q/semester_3/surveying_i/scale-plot-39672-sqm site: BCT Engineering --- # Scale for 39672 m² plan Surveying I · Chapter 1: Introduction - Asked in: 2075 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-39672-sqm - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-1 ## Question A plan represents an area of 39672 m² and represents 4.75 cm × 5.22 cm on plan. Find the scale of the plot and indicate through a sketch how a suitable scale can be constructed to read up to 1 m on the plan. The scale should be long enough to measure upto 400 m. ## Short answer RF is 1/4000. A diagonal scale 10 cm long reads 1 m up to 400 m; use four 100 m divisions of 2.5 cm plus one left subdivision for 10 m. Diagonals give 1 m steps. ## Answer #### RF Map area $= 4.75 \times 5.22 = 24.795$ cm$^2$. Ground area $= 39672 \times 10^{4} = 3.9672 \times 10^{8}$ cm$^2$. $$ \text{RF}^2 = \frac{24.795}{3.9672 \times 10^{8}} = 6.25 \times 10^{-8}, \qquad \text{RF} = 2.5 \times 10^{-4} = \frac{1}{4000} $$ #### Scale (to read 1 m, up to 400 m) $$ \text{Length} = \frac{400 \times 100}{4000} = 10\ \text{cm} $$ 100 m $= 2.5$ cm, 10 m $= 0.25$ cm, 1 m $= 0.025$ cm. This is a diagonal scale. #### Sketch and construction 1. Draw a 10 cm line divided into 4 main divisions of 2.5 cm (100 m each); add one division to the left of 0. 2. Divide the left division into 10 parts of 0.25 cm (10 m). 3. Draw 10 horizontal lines (height 2.5 cm) and the diagonals from the top of each sub-division to the next lower sub-division at the base. 4. Each step along a diagonal = 1 m. ```text 10 | / / / / / / / / / / | 5 | / / | 0 +---+----+----+----+----+--------+ 90..0 100 200 300 400 (m) ``` **Answer: RF = 1/4000; scale length = 10 cm.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the RF found when map area and ground area are known? A. RF = map area / ground area B. RF = square root of (map area / ground area), both in the same units C. RF = (map area / ground area)^2 D. RF = ground area / map area Answer: B. Area varies as the square of the linear scale, so RF^2 = map area / ground area and RF is its square root. (Key point: RF from areas) 2. Why is the ground area 39672 m^2 multiplied by 10^4 before finding the RF? A. To convert m^2 to cm^2 so it matches the map area in cm^2 B. To convert hectares to m^2 C. To convert the area to km^2 D. To apply the square root Answer: A. 1 m^2 = 10^4 cm^2, and both areas must be in the same unit before taking the ratio. (Key point: Unit conversion) 3. With RF = 1/4000, what length of line is needed to represent 400 m? A. 2.5 cm B. 4 cm C. 10 cm D. 16 cm Answer: C. Length = 400 x 100 / 4000 = 10 cm. (Key point: Length of scale) 4. Why is a diagonal scale needed to read up to 1 m here? A. Because 400 m is too long for a plain scale B. Because 1 m is only 0.025 cm on the plan, too small to divide directly C. Because the RF is a fraction D. Because the plot is rectangular Answer: B. A plain scale cannot show 0.025 cm; diagonals subdivide the 10 m division into 1 m steps. 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