Question

Right Rectangular Prisms & Pyramids Unit Test
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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

8,333.33 ft.3
8,333.33 feet cubed

95 ft.3
95 feet cubed

25,000 ft.3
25,000 feet cubed

75,000 ft.3

Answer 1

To find the volume of a pyramid, we can use the formula:

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

In this case, the base is a rectangle, so we first find the area of the base:

\[
\text{Base Area} = \text{length} \times \text{width} = 50\, \text{ft} \times 20\, \text{ft} = 1000\, \text{ft}^2
\]

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

Now we can calculate the volume:

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

\[
\text{Volume} = \frac{1}{3} \times 25000\, \text{ft}^3 = 8333.33\, \text{ft}^3
\]

So the lagoon holds **8,333.33 feet cubed** (or 8,333.33 ft³).

The answer is:

**8,333.33 ft.³**