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)

Question

Responses

75,000 ft.3
75,000 feet cubed

8,333.33 ft.3
8,333.33 feet cubed

25,000 ft.3
25,000 feet cubed

95 ft.3

Answer 1

To find the volume of the upside-down pyramid-shaped 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 top 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. Identify the height: The deepest point of the lagoon is 25 feet, which is the height of the pyramid.

3. Calculate the volume:

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

Thus, the lagoon holds 8,333.33 ft³ of water.

The correct response is:

8,333.33 ft³