To determine the volume of the upside down pyramid-shaped lagoon, we can use the formula for the volume of a pyramid, which is:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base of the pyramid (the top of the lagoon) is a rectangle measuring 50 feet by 20 feet.
- First, calculate the area of the base:
\[ \text{Base Area} = \text{Length} \times \text{Width} = 50 , \text{ft} \times 20 , \text{ft} = 1000 , \text{ft}^2 \]
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The height of the pyramid (the depth of the lagoon) is 25 feet.
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Now, substitute these values into the volume formula:
\[ V = \frac{1}{3} \times 1000 , \text{ft}^2 \times 25 , \text{ft} \]
\[ V = \frac{1}{3} \times 25000 , \text{ft}^3 \]
\[ V = \frac{25000}{3} , \text{ft}^3 \approx 8333.33 , \text{ft}^3 \]
Thus, the volume of the lagoon is approximately 8333.33 ft³.
So, the correct response is:
8,333.33 ft.³
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