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 tje lagoon is 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 pyramid and subtract the volume of the rectangular portion on top.
The volume of a pyramid is given by the formula: V = (1/3) * base area * height
The base area of the pyramid is equal to the area of the rectangle on top, so it is 50 feet * 20 feet = 1000 square feet.
The height of the pyramid is the distance from the top of the lagoon to the deepest point, which is 25 feet.
Therefore, the volume of the pyramid is: (1/3) * 1000 square feet * 25 feet = 8333.33 cubic feet.
The volume of the rectangular portion on top is simply the length * width * height = 50 feet * 20 feet * 25 feet = 25000 cubic feet.
So, the total volume of water the lagoon holds is: 8333.33 cubic feet - 25000 cubic feet = -16666.67 cubic feet.
However, negative volume does not make sense in this context, so we can conclude that there was an error in the calculations or the values given.
To find the volume of the scuba diving lagoon, we need to calculate the volume of the solid shape formed by an upside-down pyramid with a rectangular base.
To do this, we will consider the pyramid as two parts: a rectangular prism on top (the shallow end) and a smaller pyramid-shaped portion at the bottom (the deep end).
1. Calculate the volume of the rectangular prism:
Volume of a rectangular prism = length × width × height
Volume of the rectangular prism = 50 ft × 20 ft × 25 ft = 25,000 cubic feet
2. Calculate the volume of the pyramid:
Volume of a pyramid = (1/3) × base area × height
The base area of the pyramid is equal to the area of the rectangle, which is 50 ft × 20 ft = 1,000 square feet.
Volume of the pyramid = (1/3) × 1,000 sq ft × 25 ft = 8,333.33 cubic feet (rounded to the nearest hundredth).
3. Calculate the total volume of the lagoon:
Total volume = volume of the rectangular prism + volume of the pyramid
Total volume = 25,000 cubic feet + 8,333.33 cubic feet = 33,333.33 cubic feet (rounded to the nearest hundredth).
Therefore, the scuba diving lagoon holds approximately 33,333.33 cubic feet of water.