I have a water pond, 13ft deep,  bottom  is 103 by 164 ft and top is 159 by 200 ft what is the total volumen

To calculate the volume of the pond, which has a trapezoidal shape (since the bottom and top areas are different), you can use the formula for the volume of a frustum of a pyramid:

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

where:
- \( V \) is the volume,
- \( h \) is the height (depth) of the pond,
- \( A_1 \) is the area of the bottom,
- \( A_2 \) is the area of the top.

First, let's calculate the areas of the bottom (\( A_1 \)) and top (\( A_2 \)) of the pond:

\[
A_1 = 103 \, \text{ft} \times 164 \, \text{ft} = 16,892 \, \text{sq ft}
\]

\[
A_2 = 159 \, \text{ft} \times 200 \, \text{ft} = 31,800 \, \text{sq ft}
\]

Next, we calculate the volume:

\[
V = \frac{13 \, \text{ft}}{3} \times \left( 16,892 \, \text{sq ft} + 31,800 \, \text{sq ft} + \sqrt{16,892 \, \text{sq ft} \times 31,800 \, \text{sq ft}} \right)
\]

Let's calculate this step by step.The total volume of the pond is approximately **311,431.61 cubic feet**.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How would the volume change if the depth were increased by 5 feet?
2. What is the volume in gallons?
3. How can we calculate the surface area of the pond?
4. How does the shape of the pond affect its volume compared to a simple rectangular prism?
5. What would be the volume if both the top and bottom dimensions were the same?

**Tip:** When dealing with irregularly shaped objects like your pond, using the frustum formula is key to accurately calculating the volume.

Learn how to calculate the volume of a trapezoidal pond with a depth of 13 feet, bottom dimensions of 103 by 164 feet, and top dimensions of 159 by 200 feet. Detailed step-by-step solution using the frustum volume formula. Ideal for high school students studying geometry and volume calculations.

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