Q.NO#01: The plan of an old survey plotted to a scale of 10 m to 1 cm was found to have shrunk so that a line originally 10 cm long was found to measure 9.8 cm. There was also a note on the plan that the 30 m chain used in the survey was 0.03 m too short.If the area of the plan measured now with a planimeter is 96.04 cm2 .Determine the true area of the survey?

1. Ghulam Mehdi CMSID@23101
1
Formula Used
 True Length= (Wrong Scale/Correct Scale) *Measured Length
 True Area= (Wrong Chain Used/Correct Chain Used)2 * Calculated Area
 Calculated Area=Original Area *(Scale Used)2
Q.NO#01: The plan of an old survey plotted to a scale of 10 m to 1 cm was found to have
shrunk so that a line originally 10 cm long was found to measure 9.8 cm.
There was also a note on the plan that the 30 m chain used in the survey was 0.03 m too
short.If the area of the plan measured now with a planimeter is 96.04 cm2 .Determine the true
area of the survey?
Ans: Given Data:
Measured Length=96.04 cm2
Wrong Scale=10 cm
Correct Scale=9.8 cm
Original Area=?
Calculated Area=?
True Area=?
Sol:
We know that
Original Area= (Wrong Scale/Correct Area) *Measured Length
Putting values, We have:
Original Area=(10/9.8)2 *96.04
Original Area=100 cm2………………………………………….(i)
While calculated area will be,
Calculated Area=Original Area *(Scale Used)2
Putting values, We have:
Calculated Area=100 *100
Calculated Area=10000 m2……………………………………….(ii)
And
True Area=(Wrong Chain Used/Correct Chain Used)2 * Calculated Area
Putting values, We have:
True Area=(29.97/30)2 *10000
True Area=9980.01 m2………………………………………..Ans