Civil Engineering - UPSC Civil Service Exam Questions - Discussion

Discussion Forum : UPSC Civil Service Exam Questions - Section 1 (Q.No. 18)
18.
A plot of land 60°m x 20 m is measure steel tape. If the standard error of length width measurements is taken as ± 1 cm, the standard error of the area of the plot be
± 0.1414 m2
± 0.566 m2
± 0.632 m2
± 0.8484 m2
Answer: Option
Explanation:
No answer description is available. Let's discuss.
Discussion:
7 comments Page 1 of 1.

Mushtaq Ahmad said:   3 years ago
@All.

Simple Formula to remember;

Error in Area= {(error in length + length of plot) ^2 + (error in width + width of plot) ^2}.

And then take the square root of the result.
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Arpon said:   7 years ago
Here, error = √[ {(length)^2 * (error in length)^2} + {(width)^2 * (error in width)^2}].
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Arpon said:   7 years ago
How ? can't understand. Please explain.
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Rakesh said:   8 years ago
Please give correct explanation to understand the solution.
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Abhay said:   9 years ago
Std Error of A = σA = Sqrt{(δA/δX)2σX2+ (δA/δY)2σY2}

A = X * Y.

X = 60 +/- 0.01m , Y = 20m +/- 0.01m.

Since [(δA/δX) = Y and (δA/δY) = X.

Substituting value of X and Y with either +ve error or -ve error.

σA = Sqrt{Y2*(0.01)2 + X2*(0.01)2}

= +/- 0.6325.

Raj said:   9 years ago
standard error of A = ^,A = SQRT[(^,A/^,X)^2 ^,X^2+(^,A/^,Y)^2 ^,Y^2].

Pranay said:   9 years ago
How? Please explain.
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