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?
a 8,333.33 ft^3
b 25,000 ft^3
c 95 ft^3
d 75,000 ft^3
To find the volume of the lagoon, we need to calculate the volume of each individual pyramid making up the shape.
The top rectangle of the lagoon has dimensions of 50 feet by 20 feet, so its area is 50 * 20 = 1000 square feet.
The height of the pyramid, from the top rectangle to the deepest point (in the middle at 25 feet), is 25 feet.
The volume of a pyramid is given by the formula (1/3) * base area * height.
So the volume of each individual pyramid is (1/3) * 1000 * 25 = 8333.33 cubic feet.
Since the lagoon is composed of four identical pyramids stacked on top of each other, the total volume of the lagoon is 4 * 8333.33 = 33333.33 cubic feet.
Therefore, the correct answer is a) 8,333.33 ft^3.