To calculate the volume of earthwork for an embankment, we can use the formula for the volume of a prismoidal shape, as the embankment consists of a trapezoidal cross-section that extends along a certain length.

Here are the steps:

Step 1: Determine the Area of the Cross-section

The cross-section of the embankment is trapezoidal. The area of a trapezoid can be calculated as:

$A = \frac{1}{2} \times \left(B_1 + B_2\right) \times h$

Where:

• $B_1$ is the width of the top (formation level) = 8 m,
• $B_2$ is the width of the bottom, which we need to calculate considering the side slopes,
• $h$ is the depth of cutting (height) = 5 m.

Step 2: Calculate the Bottom Width

For each slope, we need to account for the horizontal distance that the slope adds on both sides:

• On one side, the slope is 1:2, meaning the horizontal distance is $2 \times 5 = 10 \text{ m}$,
• On the other side, the slope is 1:3, meaning the horizontal distance is $3 \times 5 = 15 \text{ m}$.

Thus, the total width at the bottom is: $B_2 = 8 + 10 + 15 = 33 \text{ m}.$

Step 3: Calculate the Area of the Cross-section

Now, we can substitute the values into the trapezoidal area formula:

$A = \frac{1}{2} \times (8 + 33) \times 5 = \frac{1}{2} \times 41 \times 5 = 102.5 \text{ m}^2.$

Step 4: Calculate the Volume

The total volume is the cross-sectional area multiplied by the length of the embankment (250 m):

$V = 102.5 \times 250 = 25,625 \text{ m}^3.$

Thus, the correct volume of the earthwork is:

$\boxed{25,625 \text{ m}^3}.$

The correct answer is: c. 25,625 m³

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Would you like more details or have any questions?

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Here are 5 related questions:

1. How would the volume change if the formation level width increased to 10 m?
2. What if the depth of cutting was reduced to 4 m with the same slopes?
3. How would different slope ratios affect the volume calculation?
4. Can the same formula be used for irregular cross-sections? Why or why not?
5. How is the prismoidal method applied to more complex geometries?

Tip: Always verify the unit consistency in any geometric or earthwork problem. Mixing units can lead to errors!