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?
1. 8,333.33 ft^3
2. 95 ft^3
3. 75,000 ft^3
4. 25,000 ft^3
To find the volume of the lagoon, we need to calculate the volume of each section of the lagoon and add them together.
First, we find the volume of the rectangular top section. The formula for the volume of a rectangular prism is length x width x height. In this case, the length is 50 feet, the width is 20 feet, and the height is 25 feet (the depth of the lagoon at its deepest point).
Therefore, the volume of the rectangular section is 50 ft x 20 ft x 25 ft = 25,000 ft^3.
Next, we need to find the volume of the two triangular sections on the sides of the lagoon. Since the shape is an upside-down pyramid, the formula for the volume of a pyramid is (1/3) x base area x height. In this case, the base area of each triangular section is (1/2) x 20 ft x 25 ft = 250 ft^2 (since the width is the same as the width of the rectangular top section and the height is the same as the depth). The height of each triangular section is 25 ft.
Therefore, the volume of each triangular section is (1/3) x 250 ft^2 x 25 ft = 2,083.33 ft^3.
Finally, we add the volumes of all three sections together to get the total volume of the lagoon:
25,000 ft^3 + 2,083.33 ft^3 + 2,083.33 ft^3 = 29,166.66 ft^3
Therefore, the correct answer is 29,166.66 ft^3, which is not one of the options given.
may you please pick one answer bot its for a test <3
Sure! Based on the options provided, the closest answer is 25,000 ft^3.
To find the volume of the scuba diving lagoon, we need to calculate the volume of the shape and subtract the volume of the empty space above it.
The shape is an upside-down pyramid, which consists of a rectangular top and four triangular sides. The volume formula for a pyramid is 1/3 * base area * height.
First, let's find the base area of the pyramid, which is the area of the rectangular top. The base area is length * width = 50 ft * 20 ft = 1000 ft^2.
Next, let's find the height of the pyramid. The deepest point of the lagoon is in the middle at 25 ft deep. Since it is an upside-down pyramid, the height of the pyramid is half of the depth, so the height is 25 ft / 2 = 12.5 ft.
Now we can calculate the volume of the pyramid:
Volume = 1/3 * base area * height
Volume = 1/3 * 1000 ft^2 * 12.5 ft
Volume = 41,666.67 ft^3
However, this volume includes the empty space above the lagoon. To find the actual water volume, we need to subtract the empty space. The empty space is another pyramid with the same base area and a height equal to the height above the water level (25 ft).
The volume of the empty space pyramid is:
Volume empty space = 1/3 * base area * height empty space
Volume empty space = 1/3 * 1000 ft^2 * 25 ft
Volume empty space = 8,333.33 ft^3
Finally, we subtract the empty space volume from the volume of the pyramid to get the water volume:
Water volume = Volume - Volume empty space
Water volume = 41,666.67 ft^3 - 8,333.33 ft^3
Water volume = 33,333.34 ft^3
Therefore, the lagoon holds approximately 33,333.34 ft^3 of water.
So, none of the given answer choices is correct.