Ghulam Mehdi CMSID@23101

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 thatOriginal Area= (Wrong Scale/Correct Area) *Measured LengthPutting 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 *100Calculated Area=10000 m2……………………………………….(ii)AndTrue Area=(Wrong Chain Used/Correct Chain Used)2 * Calculated AreaPutting values, We have:

True Area=(29.97/30)2 *10000True Area=9980.01 m2………………………………………..Ans

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