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

25,000 ft.3
25,000 feet cubed

75,000 ft.3
75,000 feet cubed

8,333.33 ft.3
8,333.33 feet cubed

95 ft.3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the lagoon, we can calculate the volume of each section and then add them together.

The top of the lagoon is a rectangle that is 50 feet by 20 feet, so its volume is:

50 ft * 20 ft = 1000 ft^2

The deepest point of the lagoon is 25 feet deep. Since the lagoon is in the shape of an upside down pyramid, we can calculate the volume of this section using the formula for the volume of a pyramid:

V = (1/3) * base area * height

For this section, the base area is the same as the top of the lagoon (1000 ft^2) and the height is 25 ft, so the volume is:

V = (1/3) * 1000 ft^2 * 25 ft = 8333.33 ft^3

So, the total volume of the lagoon is:

1000 ft^2 + 8333.33 ft^3 = 9333.33 ft^3

Therefore, the correct answer is 8,333.33 ft^3.