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 point)
Responses
75,000 ft.3
75,000 feet cubed
25,000 ft.3
25,000 feet cubed
95 ft.3
95 feet cubed
8,333.33 ft.3
To find the volume of the scuba diving lagoon, we first need to calculate the volume of the rectangle at the top and the volume of the pyramid-like structure below it.
The volume of a rectangle is calculated by multiplying its length, width, and height. The length and width of the rectangle are given as 50 feet and 20 feet, respectively. However, we need to consider that the depth/height is only half of the overall depth of the lagoon, which is 25 feet deep. Therefore, the height of the rectangle is 25/2 = 12.5 feet.
Volume of rectangle = length x width x height
Volume of rectangle = 50 ft x 20 ft x 12.5 ft = 12,500 ft^3.
The volume of a pyramid is calculated by multiplying the area of its base by its height and dividing by 3. The base of the pyramid is the rectangle at the top, which measures 50 feet by 20 feet. Again, we need to consider that the height of the pyramid is only half of the overall depth of the lagoon, which is 25 feet deep. Therefore, the height of the pyramid is 25/2 = 12.5 feet.
Area of base = length x width
Area of base = 50 ft x 20 ft = 1000 ft^2.
Volume of pyramid = (area of base x height) / 3
Volume of pyramid = (1000 ft^2 x 12.5 ft) / 3 = 4,166.67 ft^3.
To find the total volume of the lagoon, we add the volume of the rectangle and the volume of the pyramid.
Total volume of lagoon = volume of rectangle + volume of pyramid
Total volume of lagoon = 12,500 ft^3 + 4,166.67 ft^3 = 16,666.67 ft^3.
Therefore, the lagoon holds approximately 16,666.67 ft^3 of water.
bot use one of the options
According to the given options, the correct answer is:
16,666.67 ft.3
bot use one of these for the answer
According to the given options, the answer is:
8,333.33 ft.3