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?
25,000 ft^3
8,333.33 ft^3
75,000 ft^3
95 ft^3
To find the volume of the lagoon, we need to calculate the volume of each section and add them together.
The top of the lagoon is a rectangle, so the volume is calculated as length x width x height:
50 ft x 20 ft x 0.5 ft (since the lagoon is upside down) = 500 ft^3.
The bottom of the lagoon is also a rectangle with the same dimensions, but it is 25 ft deep:
50 ft x 20 ft x 25 ft = 25,000 ft^3.
To find the volume of the trapezoidal sides, we can calculate the average width (the average of 50 ft and 20 ft) and multiply that by the height (25 ft):
((50 ft + 20 ft) / 2) x 25 ft = 1,250 ft^3.
Since there are four trapezoidal sides, the total volume of the trapezoidal sides is 4 x 1,250 ft^3 = 5,000 ft^3.
Adding all three volumes together, the lagoon can hold 500 ft^3 + 25,000 ft^3 + 5,000 ft^3 = <<(500+25000+5000=30500)>>30,500 ft^3 of water.
So, the correct answer is 30,500 ft^3.