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)
8, 333.33ft .^ 3
O95 ft.
O 75000ft .^ 3
25000ft .^ 3
To calculate the volume of the lagoon, we need to find the volume of the rectangular top section and then subtract the volume of the pyramid at the bottom.
The volume of the rectangular top section is calculated by multiplying the length, width, and depth:
Volume of the rectangular top section = 50 ft * 20 ft * 25 ft = 25,000 ft³
The volume of the pyramid at the bottom can be calculated using the formula for the volume of a pyramid:
Volume of the pyramid = (1/3) * base area * height
The base area of the pyramid is the same as the rectangular top section, so it is 50 ft * 20 ft = 1,000 ft².
The height of the pyramid is the depth at the deepest point, which is 25 ft.
Volume of the pyramid = (1/3) * 1,000 ft² * 25 ft = 8,333.33 ft³
To find the total volume of the lagoon, we subtract the volume of the pyramid from the volume of the rectangular top section:
Total volume = 25,000 ft³ - 8,333.33 ft³ = 16,666.67 ft³
Therefore, the lagoon holds approximately 16,666.67 ft³ of water.