Discussion
A tank is excavated in a level ground to a depth of 8 m with uniform side slopes. The top of the tank at ground level is rectangular in shape of size 40 × 20 m, while the bottom is of size 24 × 12 m. Compute the volume of earthwork by the trapezoidal rule.
Answer: D
The volume of earthwork by the trapezoidal rule is the mean of the end areas times the depth. The top area is \(40 \times 20 = 800\) m\(^2\) and the bottom area is \(24 \times 12 = 288\) m\(^2\):
\[ \begin{aligned} V = \frac{800 + 288}{2} \times 8 = 544 \times 8 \\ &= 4352\ \text{m}^3 \end{aligned} \]The prismoidal formula would give a slightly smaller value (about 4181 m\(^3\)), and the other options are different from both rules.
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