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’ x 20’, and the deepest point of the lagoon is in the middle at 25 feet deep. How much water does the lagoon hold?
To calculate the volume of the lagoon, we need to find the volume of the rectangular top and subtract the volume of the upside-down pyramid.
The volume of the rectangular top is given by:
Volume_top = length * width * height
where length = 50 feet, width = 20 feet, and height = 0 feet (since it is a rectangle).
Volume_top = 50 * 20 * 0 = 0 cubic feet
The volume of the upside-down pyramid can be calculated using the formula:
Volume_pyramid = (1/3) * base_area * height
The base area is obtained by multiplying the length and width of the rectangular top, and the height is the difference between the width at the top (20 ft) and the width at the bottom (0 ft).
Base_area = length * width = 50 * 20 = 1000 square feet
Height = 20 ft - 0 ft = 20 feet
Volume_pyramid = (1/3) * 1000 * 20 = 6666.67 cubic feet
Thus, the total volume of water the lagoon can hold is given by:
Total Volume = Volume_top - Volume_pyramid = 0 - 6666.67 = -6666.67 cubic feet
It's important to note that since the top area is 0, it is not possible for the lagoon to have a negative volume. Therefore, there might be an error in the given dimensions or the shape of the lagoon.