Question

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 in the deepest point of the lagoon is in the middle at 25 feet deep. How much water does the lagoon hold

Answer 1

To find the volume of the lagoon, we need to calculate the volume of the rectangular top and then subtract the volume of the pyramid.

The volume of the rectangular top is given by:

Volume_rectangular_top = length * width * depth
Volume_rectangular_top = 50 ft * 20 ft * 25 ft
Volume_rectangular_top = 25,000 ft³

The volume of the pyramid can be calculated using the formula:

Volume_pyramid = (1/3) * base_area * height
Base_area = length * width
Height = 25 ft

Volume_pyramid = (1/3) * (50 ft * 20 ft) * 25 ft
Volume_pyramid = 1/3 * 1000 ft² * 25 ft
Volume_pyramid = 8,333.333 ft³ (rounded to three decimal places)

Now, let's find the total volume of the lagoon by subtracting the volume of the pyramid from the volume of the rectangular top:

Volume_lagoon = Volume_rectangular_top - Volume_pyramid
Volume_lagoon = 25,000 ft³ - 8,333.333 ft³
Volume_lagoon = 16,666.667 ft³ (rounded to three decimal places)

Therefore, the lagoon holds approximately 16,666.667 cubic feet of water.