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RF and scale for 51072 m² plot

Short answer

RF is 1/5000. A diagonal scale of length 12 cm is needed to read 1 m up to 600 m, with 100 m divisions of 2 cm and 10 m subdivisions. It is constructed with 10 horizontal lines and diagonals giving 1 m steps.

A map is drawn to some scale so that a plot of 51072 m² is represented by 4.56 cm × 4.48 cm on the plan. Calculate the suitable RF of scale of the map and draw a scale to read upto a metre from the map; the scale should be long enough to measure upto 600 m.

RF from the area

Area on map =4.56×4.48=20.4288= 4.56 \times 4.48 = 20.4288 cm2^2. Ground area =51072= 51072 m2^2 =51072×104= 51072 \times 10^{4} cm2=5.1072×108^2 = 5.1072 \times 10^{8} cm2^2.

RF2=20.42885.1072×108=4.0×10−8\text{RF}^2 = \frac{20.4288}{5.1072 \times 10^{8}} = 4.0 \times 10^{-8} RF=2×10−4=15000\text{RF} = 2 \times 10^{-4} = \frac{1}{5000}

Scale

Length for 600 m =600×1005000=12= \dfrac{600 \times 100}{5000} = 12 cm. Here 100 m =2= 2 cm, 10 m =0.2= 0.2 cm and 1 m =0.02= 0.02 cm. Since 1 m is only 0.2 mm on the map, a diagonal scale is needed.

Construction

  1. Draw a 12 cm line and divide it into 6 main divisions of 2 cm (100 m each). Mark 0 at the end of the first (left) division and number the others 100, 200, ... 500.
  2. Divide the left division into 10 parts of 0.2 cm (10 m each).
  3. Draw 10 equally spaced horizontal lines (total height, say, 2 cm), erect perpendiculars at each main division, and draw diagonals from the top of each sub-division to the next lower sub-division on the base. The steps along the diagonals read 1 m.
 10 |  /  /  /  /  /  /  /  /  /  /  |
  5 | /  /                            |
  0 +---+---+---+---+---+---+---+---+-+
   90..0  100  200  300  400  500 (m)

Answer: RF = 1/5000; diagonal scale length = 12 cm, reading 1 m up to 600 m.

✓ Answer checked by Claude Opus 5.5 (high effort)

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