a trapezoidal ditch measures 20 feet across the top 16 feet across the bottom 12 feet deep and 3 miles long. how much water will this ditch hold when it is full

To determine how much water the trapezoidal ditch can hold when full, we need to calculate the volume of the ditch. The ditch can be treated as a trapezoidal prism.

### Step 1: Area of the trapezoidal cross-section
The area \( A \) of a trapezoid is calculated using the formula:

\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]

Where:
- \( b_1 = 20 \) feet (the length of the top base)
- \( b_2 = 16 \) feet (the length of the bottom base)
- \( h = 12 \) feet (the height, or depth, of the ditch)

Substituting the values:

\[
A = \frac{1}{2} \times (20 + 16) \times 12 = \frac{1}{2} \times 36 \times 12 = \frac{1}{2} \times 432 = 216 \text{ square feet}
\]

### Step 2: Volume of the trapezoidal prism
The volume \( V \) of the trapezoidal prism is found by multiplying the area of the cross-section by the length \( L \) of the ditch:

\[
V = A \times L
\]

The length of the ditch is 3 miles. Converting this to feet:

\[
L = 3 \times 5280 = 15840 \text{ feet}
\]

Substituting the values:

\[
V = 216 \times 15840 = 3,422,400 \text{ cubic feet}
\]

### Conclusion
The ditch will hold **3,422,400 cubic feet** of water when full.

Would you like more details or have any questions?

### Related Questions
1. How do you convert cubic feet of water to gallons?
2. What is the formula for the volume of other prisms, like a triangular or rectangular prism?
3. How would the volume change if the depth of the ditch were increased?
4. How do you calculate the area of a trapezoid with unequal sides?
5. What is the difference between a trapezoid and a trapezium?

### Tip
Always make sure to convert all measurements to the same unit before performing any calculations involving volume or area.

Learn how to calculate the volume of a trapezoidal ditch with dimensions 20 feet across the top, 16 feet across the bottom, and 12 feet deep. Detailed step-by-step solution included. Suitable for students in Grades 7-9.

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