Question

Corey built a pool. How many cubic feet of water can fit in the pool?
Solve on paper, then enter your answer on Zearn. You can use the calculator to help you solve.
Right trapezoidal prism with side lengths labeled: 5 ft, 18 ft, 25 ft, and 10 ft.
Corey's pool
cubic feet of water can fit in the pool.

Answer 1

To find the volume of water that can fit in Corey's right trapezoidal prism-shaped pool, we need to first calculate the area of the trapezoidal base and then multiply it by the height (or length) of the prism.

1. **Identify the dimensions**:
The trapezoidal base has parallel sides of 5 ft and 18 ft, and the height of the trapezoid (the distance between the two parallel sides) seems to be 10 ft (the given dimension for the rectangle perpendicular to these two sides). The height of the prism (the length along its depth) is given as 25 ft.

2. **Calculate the area of the trapezoidal base**:
The formula for the area \( A \) of a trapezoid is:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides and \( h \) is the height (distance between the sides).

In our case:
- \( b_1 = 5 \, \text{ft} \)
- \( b_2 = 18 \, \text{ft} \)
- \( h = 10 \, \text{ft} \)

Plugging in these values:
\[
A = \frac{1}{2} \times (5 + 18) \times 10 = \frac{1}{2} \times 23 \times 10 = \frac{230}{2} = 115 \, \text{sq ft}
\]

3. **Calculate the volume of the prism**:
The volume \( V \) of a prism is given by:
\[
V = A \times \text{height}
\]
In this case, the height (or length) of the prism is 25 ft.

Thus:
\[
V = 115 \, \text{sq ft} \times 25 \, \text{ft} = 2875 \, \text{cubic feet}
\]

So, the volume of water that can fit in Corey's pool is **2875 cubic feet**.