Question Bank • QB_SWCE_SUR_005 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Surveying and Levelling

Subtopic: Computation of areas and volume

Question Statement:

Using Simpson's $1/3$rd rule, calculate the area in $\text{m}^2$ of an irregular tract bounded by a base line and five equidistant perpendicular offsets spaced at intervals of $d = 10\text{ m}$: $y_0 = 4.0\text{ m}, y_1 = 6.0\text{ m}, y_2 = 8.0\text{ m}, y_3 = 7.0\text{ m}, y_4 = 5.0\text{ m}$. Round off to 1 decimal place ________.

Answer Key:

256.7

Step-by-Step Solution & Explanation

Simpson's $1/3$rd rule for 5 offsets (4 equal intervals of $d = 10\text{ m}$): $A = \frac{d}{3} [ (y_0 + y_4) + 4(y_1 + y_3) + 2(y_2) ]$ Substituting offsets: • End offsets: $y_0 + y_4 = 4.0 + 5.0 = 9.0\text{ m}$ • Odd offsets: $y_1 + y_3 = 6.0 + 7.0 = 13.0\text{ m} \implies 4(13.0) = 52.0$ • Even offset: $y_2 = 8.0\text{ m} \implies 2(8.0) = 16.0$ $\text{Bracket sum} = 9.0 + 52.0 + 16.0 = 77.0$ $A = \frac{10}{3} \times 77.0 = \frac{770}{3} \approx 256.67\text{ m}^2 \approx 256.7\text{ m}^2$
← Previous (QB_SWCE_ADV_138) Next (QB_SUB_SWCE_0390) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test