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
95 ft.3
95 feet cubed
8,333.33 ft.3
To find the volume of the lagoon, we need to find the volume of each level of the pyramid and then add them together.
First, let's find the volume of the rectangle at the top of the lagoon. The volume of a rectangular prism is given by the formula V = length * width * depth. In this case, the length is 50 feet, the width is 20 feet, and the depth is 0 feet (since it is at the surface). Therefore, the volume of the rectangle is 50 * 20 * 0 = 0 ft^3.
Next, let's find the volume of the pyramid. The volume of a pyramid is given by the formula V = (1/3) * base area * height. In this case, the base area is the same as the area of the rectangle, which we already found to be 50 * 20 = 1000 ft^2. And the height of the pyramid is half of the depth of the lagoon, which is 25 feet. Therefore, the volume of the pyramid is (1/3) * 1000 * 25 = 8333.33 ft^3.
Finally, let's add the volume of the rectangle and the pyramid. 0 + 8333.33 = 8333.33 ft^3. Therefore, the lagoon holds approximately 8333.33 ft^3 of water.
So the correct answer is 8,333.33 ft.3