Question

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 95 ft.3 95 feet cubed 8,333.33 ft.3 8,333.33 feet cubed 25,000 ft.3 25,000 feet cubed 75,000 ft.3

Answer 1

To find the volume of the scuba diving lagoon, which is shaped like an upside-down pyramid, 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 a length of 50 feet and a width of 20 feet.

   \[ \text{Base Area} = \text{Length} \times \text{Width} = 50 , \text{ft} \times 20 , \text{ft} = 1000 , \text{ft}^2 \]

2. Identify the height: The height of the pyramid corresponds to the depth of the lagoon, which is 25 feet.

3. Calculate the volume: Now we can substitute the base area and the height into the volume formula.

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

So, the volume of water that the lagoon can hold is:

\[ \text{Volume} \approx 8,333.33 , \text{ft}^3 \]

The correct response is 8,333.33 ft.³.