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)
A: 25,000 ft^3
B: 95 ft^3
C: 75,000 ft^3
D: 8,333.33 ft^3
To find the volume of the lagoon, we need to find the volume of the rectangular top and subtract the volume of the missing pyramid shape.
The volume of the rectangular top is equal to length times width times depth: 50 ft x 20 ft x 25 ft = 25,000 ft^3.
The volume of the missing pyramid shape can be calculated using the formula for the volume of a pyramid: (1/3) x base area x height. Since the base area is the same as the rectangular top (50 ft x 20 ft), and the height is half of the depth of the lagoon (25 ft/2 = 12.5 ft), the volume of the missing pyramid shape is (1/3) x (50 ft x 20 ft) x 12.5 ft = 8,333.33 ft^3.
Therefore, the total volume of the lagoon is 25,000 ft^3 - 8,333.33 ft^3 = 16,666.67 ft^3.
The closest answer choice is D: 8,333.33 ft^3.