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 the deepest point of the lagoon is in the middle at 25 feet deep. How much water does the lagoon hold?(1 point)
Responses
95 ft.3
95 feet cubed
25,000 ft.3
25,000 feet cubed
8,333.33 ft.3
8,333.33 feet cubed
75,000 ft.3
To calculate the volume of the scuba diving lagoon, we need to find the volume of each section and then add them together.
The top of the lagoon is a rectangle with dimensions 50 feet by 20 feet. Therefore, the volume of the top section is:
Volume = length x width x depth
Volume = 50 ft x 20 ft x 25 ft = 25,000 ft^3
The bottom of the lagoon is also a rectangle with dimensions 50 feet by 20 feet. However, its depth is 0 feet as it is the surface of the lagoon. Therefore, the volume of the bottom section is:
Volume = length x width x depth
Volume = 50 ft x 20 ft x 0 ft = 0 ft^3
Finally, we need to find the volume of the middle section, which is a pyramid. The dimensions are not given, so we cannot calculate the volume accurately. Therefore, we cannot determine the exact volume of the middle section. However, we know that the deepest point of the lagoon is in the middle at 25 feet deep. So, the volume of the middle section would be less than the volume of the top section.
Since the bottom section is 0 ft^3 and the middle section is less than the top section, the total volume of the lagoon would be less than 25,000 ft^3. Therefore, the closest answer choice is 8,333.33 ft^3.