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RF and scale for 51750 m² plot

Short answer

RF = 1/5000. A diagonal scale 12 cm long represents 600 m and can read single metres.

A map is drawn to some scale so that a plot of 51750 m² is represented by 4.6 cm × 4.5 cm on the plan. Calculate the RF of the scale of the map. Draw a scale to read up to a single metre from the map; the scale should be long enough to measure upto 600 m.

RF

Map area =4.6×4.5=20.7= 4.6 \times 4.5 = 20.7 cm2^2. Ground area =51750×104=5.175×108= 51750 \times 10^{4} = 5.175 \times 10^{8} cm2^2.

RF2=20.75.175×108=4.0×10−8,RF=2×10−4=15000\text{RF}^2 = \frac{20.7}{5.175 \times 10^{8}} = 4.0 \times 10^{-8}, \qquad \text{RF} = 2 \times 10^{-4} = \frac{1}{5000}

Scale (to read 1 m, up to 600 m)

Length=600×1005000=12 cm\text{Length} = \frac{600 \times 100}{5000} = 12\ \text{cm}

100 m =2= 2 cm, 10 m =0.2= 0.2 cm, 1 m =0.02= 0.02 cm: a diagonal scale is needed.

Construction

  1. Draw a 12 cm line and divide it into 6 main divisions of 2 cm (100 m). Add one more division to the left of 0 and mark 0, 100 ... 600.
  2. Divide the left division into 10 parts (10 m each).
  3. Draw 10 equal horizontal lines on a rectangle (height about 2 cm).
  4. Draw diagonals joining the top of each sub-division with the next lower sub-division on the base. A diagonal step is 1 m.
 10 |  /  /  /  /  /  /  /  /  /  /  |
  5 | /  /                            |
  0 +---+----+----+----+----+----+----+
   90..0  100  200  300  400  500  600

Answer: RF = 1/5000; scale length = 12 cm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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