Question Bank • QB_SWCE_EXP_089 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Surveying and Levelling

Subtopic: Computation of areas and volume

Question Statement:

A railway embankment cutting has three cross-sectional areas spaced $20\text{ m}$ apart ($h = 20\text{ m}$): $A_0 = 40\text{ m}^2$, $A_1 = 65\text{ m}^2$, and $A_2 = 50\text{ m}^2$. Using Simpson's prismoidal rule $V = \frac{h}{3} (A_0 + 4 A_1 + A_2)$, calculate the volume of earthwork in $\text{m}^3$.

Answer Key:

2333.33

Step-by-Step Solution & Explanation

$V = \frac{20}{3} [40 + 4(65) + 50] = \frac{20}{3} [40 + 260 + 50] = \frac{20}{3} [350] = \frac{7000}{3} \approx 2333.33\text{ m}^3$
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