A resort is building a scuba diving lagoon in the shape of an upside down pyramid. The top of the lagoon is a rectangle that is 50 feet by 20 feet, and the deepest point of the lagoon is in the middle at 25 feet deep. How much water does the lagoon hold?(1 point) Responses 8,333.33 ft.3 8,333.33 feet cubed 25,000 ft.3 25,000 feet cubed 75,000 ft.3 75,000 feet cubed 95 ft.3

Answer 1

To calculate the volume of the upside down pyramid-shaped scuba diving lagoon, we can use the formula for the volume of a pyramid:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

1. Calculate the base area: The base of the lagoon is a rectangle with dimensions 50 feet by 20 feet. \[ \text{Base Area} = 50 , \text{ft} \times 20 , \text{ft} = 1000 , \text{ft}^2 \]

2. Determine the height: The height of the lagoon is 25 feet (the depth).

3. Calculate the volume: \[ V = \frac{1}{3} \times 1000 , \text{ft}^2 \times 25 , \text{ft} \] \[ V = \frac{1}{3} \times 25000 , \text{ft}^3 \] \[ V = \frac{25000}{3} , \text{ft}^3 \approx 8333.33 , \text{ft}^3 \]

Thus, the volume of the lagoon is approximately 8,333.33 feet cubed.

The correct response is: 8,333.33 feet cubed.