# Surveying Questions and Answers – Area Computation – Simpson’s Rule

This set of Surveying Multiple Choice Questions & Answers (MCQs) focuses on “Area Computation – Simpson’s Rule”.

1. Find the area of the traverse using Simpson’s rule if d= 12 m and the values of ordinates are 2.25m, 1.46m, 3.23m, 4.46m.
a) 116.88 sq. m
b) 161.88 sq. m
c) 611.88 sq. m
d) 169.54 sq. m

Explanation: The formula for Simpson’s rule can be given as Δ = (d/3)*((O0+O4) + 4*(O1+O3) + 2*(O2+O4)). On substitution, we get
Δ = (12/3)* ((2.25+4.46) + 4*(2.25+3.23) + 2*(1.46+4.46))
Δ = 161.88 sq. m.

2. Simpson’s rule assumes that boundary between the ordinates are parabolic arcs.
a) True
b) False

Explanation: In Simpson’s rule, it is assumed that the short lengths of the boundaries can form parabolic arcs. Simpson’s rule can be useful when boundary line departs from a straight line rather than a curve.

3. The results obtained are greater than which among the following?
a) Prismoidal rule
b) Trapezoidal rule
c) Rectangular rule
d) Square rule

Explanation: Due to the presence of curvature at the boundary whether it may be concave or convex towards the base line, the results are depended. It makes them greater than that obtained from the trapezoidal rule.

4. The value obtained from Simpson’s rule depends on the nature of the curve.
a) True
b) False

Explanation: The results obtained by Simpson’s rule are more accurate when compared to all cases. The results obtained by using Simpson’s rule are greater or smaller than those obtained by using the trapezoidal rule according as the curve of the boundary is concave or convex towards the base line.

5. Find the area of segment if the values of co-ordinates are given as 119.65m, 45.76m and 32.87m. They are placed at a distance of 2 m each.
a) 20.43 sq. m
b) 2.34 sq. m
c) 20.34 sq. m
d) 87.34 sq. m

Explanation: The area of the segment can be found out by using,
A = (2/3)*(O1-(O0+O2/2)). On substitution, we get
A = (2/3)*(45.76-(119.65+32.87/2))
A = -20.34 Sq. m (negative sign has no significance)
A = 20.34 sq. m.
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6. In which of the following cases, Simpson’s rule is adopted?
a) When straights are perpendicular
b) When straights are parallel
c) When straights form curves
d) When straights form parabolic arcs

Explanation: Even though Simpson’s rule assumes that short lengths of boundary between the ordinates are parabolic arcs, this method is more accurate for the case when straights act as a parallel to each other.

7. The total number of ordinates present must be___________
a) Real numbers
b) Complex
c) Even
d) Odd

Explanation: The presence of ordinates help in determining the area by substituting them in the formula provided. Odd number presence makes them calculate in an easy manner without involving tedious procedure.

8. Which of the following shapes is generally preferred in case of application of Simpson’s rule?
a) Square
b) Triangle
c) Trapezoid
d) Rectangle

Explanation: The application of Simpson’s rule generally involves usage of trapezoids which can involve as many sides as possible. To have any accuracy in the output it is recommended to consider a trapezoid.

9. Which of the following can the Simpson’s rule possess?
a) Negatives
b) Accuracy
c) Positives
d) Zero error

Explanation: Accuracy is the main plus point in case of Simpson’s rule. Due to the involvement of odd number of sides and also the procedure, the accuracy levels in this process are good enough for producing good result.

10. Which of the following indicates the formula for Simpson’s rule?
a) Δ = (d/3)*((O0+On) + 4*(O1+O3+……..) + 2*(O2+O4+……….))
b) Δ = (d/3)*((O0+On) + 2*(O1+O3+……..) + 2*(O2+O4+……….))
c) Δ = (d/3)*((O0+On) + 4*(O1+O3+……..) + 2*(O2+O4+……….))
d) Δ = (d/3)*((O0+On) + 2*(O1+O3+……..) + 4*(O2+O4+……….))

Explanation: The formula for Simpson’s rule can be given as the sum of the two end ordinates plus four times the sum of even intermediate ordinates plus twice the sum of odd intermediate ordinates, the whole multiplied by one-third the common interval between them. This can be mathematically expressed as,
Δ = (d/3)*((O0+On) + 4*(O1+O3+……..) + 2*(O2+O4+……….)).

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