Question

The formula which calculates the volume of earthwork accurately is:

• A. {Johnson’s formula}
• B. {Kirchhoff’s formula}
• C. {Trapezoidal formula}
• D. {Prismoidal formula}

Hint:

The Prismoidal formula is more precise than the Trapezoidal rule, as it considers curvature in earthwork calculations.

Answer 1

The Correct Option is D

Step 1: The Prismoidal formula is the most accurate method for computing earthwork volume, as it considers curved surface variations. Step 2: The formula is: \[ V = \frac{L}{6} \left( A_1 + 4A_m + A_2 \right) \] where: - \( A_1 \) and \( A_2 \) are the areas of two cross-sections, - \( A_m \) is the mid-section area, - \( L \) is the length between cross-sections. Step 3: The trapezoidal rule is simpler but less accurate, as it assumes a linear variation. Thus, the correct answer is (D) Prismoidal formula.