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

95 ft.3
95 feet cubed

8,333.33 ft.3
8,333.33 feet cubed

25,000 ft.3
25,000 feet cubed

75,000 ft.3

Answer 1

To calculate the volume of the upside-down pyramid (which is essentially a rectangular pyramid), we can use the formula for the volume \( V \) of a pyramid:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

In this case:

• The base of the pyramid is a rectangle with dimensions 50 feet by 20 feet.
• The area of the base (Base Area) is:

\[ \text{Base Area} = 50 , \text{feet} \times 20 , \text{feet} = 1000 , \text{square feet} \]

• The height of the pyramid is the depth of the lagoon, which is 25 feet.

Now, we can substitute these values into the volume formula:

\[ V = \frac{1}{3} \times 1000 , \text{ft}^2 \times 25 , \text{ft} \]

Calculating this gives:

\[ V = \frac{1}{3} \times 1000 \times 25 = \frac{25000}{3} \approx 8333.33 , \text{ft}^3 \]

Therefore, the lagoon holds approximately 8,333.33 cubic feet.

So the correct response is:

8,333.33 ft.³ (or 8,333.33 feet cubed).