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?
o 25,000 ft.^3
o 75,000 ft.^3
o 95 ft.^3
o 8,333.33 ft.^3
To find the volume of the lagoon, we can break it down into two parts: the top rectangle and the triangular sides.
The volume of the top rectangle can be found by multiplying the length, width, and depth:
Volume of rectangle = (50 ft) * (20 ft) * (25 ft) = 25,000 ft^3
To find the volume of the triangular sides, we need to find the area of the base and then multiply it by the depth. Since the triangular sides are symmetrical, we can find the area of one side and multiply it by 2:
Area of triangle = (1/2) * (50 ft) * (25 ft) = 625 ft^2
Volume of triangular sides = (625 ft^2) * (25 ft) * 2 = 31,250 ft^3
Now, we can add the volume of the top rectangle and the volume of the triangular sides together to find the total volume of the lagoon:
Total volume = Volume of rectangle + Volume of triangular sides
Total volume = 25,000 ft^3 + 31,250 ft^3
Total volume = 56,250 ft^3
Therefore, the lagoon holds 56,250 ft^3 of water.
pick one of the choices
I apologize for the confusion. Among the given choices, the correct answer is:
o 75,000 ft.^3
The lagoon holds 75,000 ft^3 of water.