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’ in the deepest point of the lagoon in the middle at 25 feet deep. How much water does the lagoon hold
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 below.
The volume of the rectangular top is equal to its length times its width times its depth:
Volume_top = 50 ft * 20 ft * 25 ft = 25,000 ft³
Next, we need to calculate the volume of the pyramid. To do this, we need to find the length and width of the pyramid at the bottom, which will be smaller than the length and width of the rectangular top.
The pyramid has a depth of 25 ft. Since it is an upside down pyramid, at the bottom, it will be the same length and width as the rectangular top but inverted:
Length_bottom = 50 ft
Width_bottom = 20 ft
Now we can calculate the volume of the pyramid using the formula:
Volume_pyramid = (1/3) * Length_bottom * Width_bottom * Depth
= (1/3) * 50 ft * 20 ft * 25 ft
= 8,333.33 ft³
Finally, we can find the total volume of the lagoon by subtracting the volume of the pyramid from the volume of the top:
Volume_lagoon = Volume_top - Volume_pyramid
= 25,000 ft³ - 8,333.33 ft³
≈ 16,666.67 ft³
Therefore, the lagoon holds approximately 16,666.67 cubic feet of water.