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Question

A plan of an old survey plotted to a scale of 10 m to 1 cm carried on a note stating that the chain having nominal length 30 m was 20 cm too short. It was also found that plan has shrunk so that a line originally 10 cm long was 9.69 cm. The area of the plot on the available plan was found to be 60cm2. The correct area of the plot is _______ ha.
  1. 0.63

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Solution

The correct option is A 0.63
Correct area on map = [Original length of tapeNominal length of tape]2×[1Shrinkage factor]2×area measured

Nominal length of tape = 30 m

Tape is 20 cm too short

Originally length of tape = 30 - 0.2 = 29.80 m

Shrinkage factor=Shrunk lengthOriginal length=9.6910=0.969

Correct area on map = (29.8030)2×[10.969]2×60

=63.05 cm2

correct area on ground = 63.05×100[1cm=10m1cm2=100m2]

=6305 m2=0.63 ha

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