Civil Engineering - GATE Exam Questions - Discussion
Discussion Forum : GATE Exam Questions - Section 4 (Q.No. 17)
17.
The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is
Discussion:
5 comments Page 1 of 1.
Unknown said:
8 years ago
Answer is (A): 10,000.
Explanation: Given: Modified length=9 cm, actual length=10 cm, actual relative factor=1/1000, modified area= 81 cm2, actual area=?
We know, Modified area= (modified relative factor/Actual relative factor)2*Actual area.
Actual area= Modified area/[(modified relative factor/Actual relative factor)2].
Actual area= 81/[(modified relative factor/1/1000)2].
Now, Modified length = (Modified RF/actual RF)*actual length.
9 cm = (Modified RF/1/1000) * 10.
Modified RF = 1/1111.11.
Actual area = 81/[(1/1111.11/1/1000)2]=99.99 = 100 cm.
As the actual scale is 1 cm to 10 m, hence.
Actual area = 100 * 102 = 10,000 m2.
Explanation: Given: Modified length=9 cm, actual length=10 cm, actual relative factor=1/1000, modified area= 81 cm2, actual area=?
We know, Modified area= (modified relative factor/Actual relative factor)2*Actual area.
Actual area= Modified area/[(modified relative factor/Actual relative factor)2].
Actual area= 81/[(modified relative factor/1/1000)2].
Now, Modified length = (Modified RF/actual RF)*actual length.
9 cm = (Modified RF/1/1000) * 10.
Modified RF = 1/1111.11.
Actual area = 81/[(1/1111.11/1/1000)2]=99.99 = 100 cm.
As the actual scale is 1 cm to 10 m, hence.
Actual area = 100 * 102 = 10,000 m2.
(3)
Sneha Mathai said:
5 years ago
Representative factor, RF = (1cm/10m) =(1/1000).
Measured area = 81cm2.
Shrinkage factor, SF = 9/10 = 0.9.
SF^2 = reduced area/actual area.
0.9^2 = 81/actual area.
Actual area = 100 cm2.
RF^2 = plan area/ground area
(1/1000)^2 = 100/ground area.
Ground area = 100 * 1000^2 cm2.
Ground area = 10000 m2.
Measured area = 81cm2.
Shrinkage factor, SF = 9/10 = 0.9.
SF^2 = reduced area/actual area.
0.9^2 = 81/actual area.
Actual area = 100 cm2.
RF^2 = plan area/ground area
(1/1000)^2 = 100/ground area.
Ground area = 100 * 1000^2 cm2.
Ground area = 10000 m2.
Shivaprasad sajjan said:
7 years ago
The scale of the original survey = 10m to 1cm.
The line originally 10cm measures 9cm.
Shrinkage factor = 9/10 = 0.9,
Reduced plan area = 81cm2.
Reduced plan area = shrinkage factor * actual plan area.
Actual plan area = 81/(0.9)^2 = 100cm2.
Actual area of survey=100*(10)^2 = 10000mts.
The line originally 10cm measures 9cm.
Shrinkage factor = 9/10 = 0.9,
Reduced plan area = 81cm2.
Reduced plan area = shrinkage factor * actual plan area.
Actual plan area = 81/(0.9)^2 = 100cm2.
Actual area of survey=100*(10)^2 = 10000mts.
(2)
Mahesh sinh said:
5 years ago
Good, thanks for explaining @Sajjan.
Shekhar chaurasia said:
5 years ago
Thanks for explaining @Sajjan.
(1)
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