Section 4: Soil and Water Conservation Engineering
Levelling, Contouring & Earthwork Volume
Subtopic: Prismoidal formula for earthwork volume
Question Statement:
For calculating earthwork volume between end cross-sectional areas $A_1$ and $A_2$ spaced distance $L$ apart with mid-section area $A_m$, the Prismoidal formula is:
Options:
(A) $V = \frac{L}{6} (A_1 + 4 A_m + A_2)$
(B) $V = \frac{L}{2} (A_1 + A_2)$
(C) $V = \frac{L}{3} (A_1 + 2 A_m + A_2)$
(D) $V = \frac{L}{4} (A_1 + A_m + A_2)$
Answer Key:
A
Step-by-Step Solution & Explanation
The Prismoidal formula (Simpson's rule for volume) gives the exact volume of a prismoid:
$V = \frac{L}{6} (A_1 + 4 A_m + A_2)$
(Note: Trapezoidal formula $V = \frac{L}{2}(A_1 + A_2)$ always overestimates prismoidal volume for concave ground shapes).