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
To calculate the volume of the lagoon, we need to find the volume of each section and then subtract the volume of the rectangular top.
The volume of a rectangular prism is found by multiplying the length, width, and height. So the volume of the rectangular top is 50 ft * 20 ft * 0 ft = 0 ft^3.
Now let's find the volume of the triangular sides. The volume of a triangular prism is found by multiplying the area of the base by the height. The base area of each triangular side is (1/2) * 50 ft * 20 ft = 500 ft^2. The height of each triangular side is 25 ft.
So the volume of each triangular side is 500 ft^2 * 25 ft = 12500 ft^3.
Since there are four triangular sides, the total volume of the triangular sides is 4 * 12500 ft^3 = 50000 ft^3.
To find the total volume of the lagoon, we need to add the volume of the rectangular top and the volume of the triangular sides. So the total volume is 0 ft^3 + 50000 ft^3 = 50000 ft^3.
Therefore, the lagoon can hold 50000 ft^3 of water.