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)

Question

Responses

25,000 ft.3
25,000 feet cubed

95 ft.3
95 feet cubed

75,000 ft.3
75,000 feet cubed

8,333.33 ft.3

Answer 1

To find the volume of the lagoon, we need to calculate the volume of the rectangular top and subtract the volume of the pyramid shape.

The volume of the rectangular top is calculated by multiplying its length, width, and depth:
Volume of rectangular top = 50 ft * 20 ft * 25 ft = 25,000 ft^3.

To find the volume of the pyramid shape, we need to calculate the average depth of the pyramid and multiply it by the base area. Since the deepest point is in the middle at 25 feet deep, the average depth is half of that, which is 12.5 feet. The base area is the same as the area of the rectangular top, which is 50 ft * 20 ft = 1,000 ft^2.

Volume of pyramid = (1/3) * base area * average depth
= (1/3) * 1,000 ft^2 * 12.5 ft
= 4,166.67 ft^3.

Therefore, the total volume of the lagoon is:

Volume of lagoon = Volume of rectangular top - Volume of pyramid
= 25,000 ft^3 - 4,166.67 ft^3
= 20,833.33 ft^3.

Therefore, the lagoon holds approximately 20,833.33 ft^3 of water. However, none of the given responses is the correct answer.