To find the volume of earth removed from the pit, we need to calculate the volume of the frustum of a trapezoidal prism. The shape of the pit is a frustum because the top and bottom are different rectangular areas.

Formula for the volume of a frustum:

$V = \frac{1}{3} \cdot h \cdot (A_1 + A_2 + \sqrt{A_1 \cdot A_2})$ Where:

• $V$ is the volume.
• $h$ is the height of the frustum (7 meters).
• $A_1$ and $A_2$ are the areas of the top and bottom faces of the frustum.
• $A_1$ is the area of the top (6m by 3m).
• $A_2$ is the area of the bottom (3m by 2m).

Step-by-step calculation:

1. Area of the top face $A_1$: $A_1 = 6 \times 3 = 18 \, \text{m}^2$

2. Area of the bottom face $A_2$: $A_2 = 3 \times 2 = 6 \, \text{m}^2$

3. Substitute values into the volume formula: $V = \frac{1}{3} \cdot 7 \cdot (18 + 6 + \sqrt{18 \times 6})$ $V = \frac{1}{3} \cdot 7 \cdot (18 + 6 + \sqrt{108})$ $V = \frac{1}{3} \cdot 7 \cdot (18 + 6 + 10.39)$ $V = \frac{1}{3} \cdot 7 \cdot 34.39$ $V = \frac{1}{3} \cdot 240.73$ $V = 80.24 \, \text{m}^3$

Thus, the volume of the earth removed from the pit is approximately 80.24 cubic meters.

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Would you like more details on any part of this solution? Let me know if you have any questions!

Here are 5 related questions:

1. How would the volume change if the height of the pit were different?
2. What is the formula for calculating the volume of a cone?
3. How do you calculate the volume of a cylinder?
4. Can the frustum formula be applied to irregular shapes?
5. How would you calculate the surface area of a frustum?

Tip: When calculating volumes for shapes with different top and bottom dimensions, remember to use the frustum formula.