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 70 feet by 40 feet and the deepest point of the lagoon is in the middle at 35 feet deep. How much water does the lagoon hold?

Answer 1

To find the volume of water the lagoon can hold, we need to calculate the volume of the upside-down pyramid (frustum) formed by it.

1. Base Area: The area of the top rectangle of the pyramid (which is a rectangle) is given by: \[ \text{Base Area} = \text{length} \times \text{width} = 70 , \text{feet} \times 40 , \text{feet} = 2800 , \text{square feet} \]

2. Height of the Pyramid: The depth of the lagoon is the height \( h \) of the pyramid: \[ h = 35 , \text{feet} \]

3. Volume of the Pyramid: The formula for the volume \( V \) of a pyramid is given by: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

4. Substituting values: \[ V = \frac{1}{3} \times 2800 , \text{sq ft} \times 35 , \text{feet} \]

5. Calculating the volume: \[ V = \frac{1}{3} \times 2800 \times 35 = \frac{98000}{3} \approx 32666.67 , \text{cubic feet} \]

Thus, the lagoon can hold approximately 32,666.67 cubic feet of water.