The pit has a trapezoidal shape, with the top and bottom being rectangular sections of different dimensions. To find the volume of earth removed, we can use the formula for the volume of a frustum of a rectangular pyramid.

Step 1: Understanding the dimensions

• Depth of the pit: 7 meters
• Top dimensions: 6 meters by 3 meters
• Bottom dimensions: 3 meters by 2 meters

Step 2: Formula for the volume of a frustum of a rectangular pyramid

The volume of a frustum of a pyramid (a truncated pyramid) is given by the formula:

$V = \frac{h}{3} \left( A_1 + A_2 + \sqrt{A_1 \times A_2} \right)$

Where:

• $h$ is the height (depth) of the pit (7 meters),
• $A_1$ is the area of the top rectangle ($6 \times 3 = 18$ square meters),
• $A_2$ is the area of the bottom rectangle ($3 \times 2 = 6$ square meters).

Step 3: Substituting the values into the formula

$V = \frac{7}{3} \left( 18 + 6 + \sqrt{18 \times 6} \right)$ $V = \frac{7}{3} \left( 18 + 6 + \sqrt{108} \right)$ $V = \frac{7}{3} \left( 18 + 6 + 10.39 \right)$ $V = \frac{7}{3} \times 34.39$ $V \approx \frac{7 \times 34.39}{3}$ $V \approx \frac{240.73}{3}$ $V \approx 80.24 \, \text{cubic meters}$

Final Answer:

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

Would you like a more detailed explanation or further steps on similar problems?

Related Questions:

1. How do you find the volume of a frustum of a cone?
2. What happens if the dimensions of the pit are all the same at the top and bottom? How does that affect the volume?
3. Can you calculate the surface area of this trapezoidal pit?
4. How would the volume change if the pit had a cylindrical shape instead of a trapezoidal one?
5. What is the formula to calculate the volume of a pyramid with a rectangular base?

Tip:

When dealing with frustum shapes, remember that the formula for the volume applies to any shape with a linear transition from one cross-section to another (rectangular, triangular, etc.). Make sure to always calculate the areas of the top and bottom cross-sections accurately!