Question

Compute the volume of excavation required to construct an excavated pond with an average depth of 5.0 m, bottom width of 15 m and bottom length of 10 m. The top area is 1000 m² and mid area of the pond is 800 m².

• A. 36.25 ha.m
• B. 3.625 ha.m
• C. 36.25 m
• D. 0.3625 ha.m

Hint:

Prismoidal formula is accurate for earthwork volume estimation.
1 ha.m = 10,000 m³ = volume of water covering 1 ha to a depth of 1 m.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The volume of an excavated pond can be calculated using the prismoidal formula.

Step 2: Key Formula:
Prismoidal formula:
\[ V = \frac{D}{6} (A_1 + 4A_m + A_2) \] Where:
V = Volume
D = Depth
A1 = Bottom area
Am = Mid area
A2 = Top area

Step 3: Detailed Explanation:
Calculate bottom area:
\[ A_1 = 10 \times 15 = 150 \mathrm{m}^2 \] Given:
D = 5.0 m
A2 = 1000 m²
Am = 800 m²
Apply the formula:
\[ V = \frac{5}{6} (150 + 4 \times 800 + 1000) \] \[ V = \frac{5}{6} (150 + 3200 + 1000) = \frac{5}{6} \times 4350 \] \[ V = \frac{21750}{6} = 3625 \mathrm{m}^3 \] Convert to hectare-meter (ha.m):
1 ha.m = 10,000 m³
\[ V = \frac{3625}{10000} = 0.3625 \text{ ha.m} \]

Step 4: Final Answer:
Thus, the volume of excavation is 0.3625 ha.m.
[0.5cm]