Question
Samira built a pool. How many cubic feet of water can fit in the pool?
Right trapezoidal prism with side lengths labeled: 5 ft, 18 ft, 25 ft, and 10 ft.
Samira's pool
cubic feet of water can fit in the pool.
Right trapezoidal prism with side lengths labeled: 5 ft, 18 ft, 25 ft, and 10 ft.
Samira's pool
cubic feet of water can fit in the pool.
Answers
Answered by
GPT-4o mini
To find the volume of water that can fit in Samira's pool, which is in the shape of a right trapezoidal prism, we first need to calculate the area of the trapezoidal base and then multiply that by the height of the prism.
### Step 1: Find 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 (bases),
- \( h \) is the height (the distance between the two bases).
In this case, let's assume:
- \( b_1 = 5 \) ft (one of the parallel sides),
- \( b_2 = 18 \) ft (the other parallel side),
- The height \( h \) between the bases can be calculated using the side lengths \( 25 \) ft and \( 10 \) ft.
However, since we only need \( h \) to calculate the area, we use the following property: in a right trapezoid, the height can directly be the vertical distance between the two parallel sides.
Assuming the height can be determined from the right trapezoid, let's assume we've determined a height based on the geometry, here's an example with common trapezoidal dimensions.
### Step 2: Calculate the area using approximate height
We do not have the height directly specified. Assuming it should be calculated, for a right trapezoid, it is often the shorter base that acts similarly. For simplicity, we can use:
\[
h = 10 \text{ ft}
\]
Now calculate the area:
\[
A = \frac{1}{2} \times (5 + 18) \times 10
\]
Calculating this gives:
\[
A = \frac{1}{2} \times 23 \times 10 = \frac{230}{2} = 115 \text{ square feet}
\]
### Step 3: Find the volume of the prism
To find the volume \( V \) of the prism, we multiply the area of the trapezoidal base by the height of the prism. If we assume the height of the prism (the depth) is, for example, 10 ft:
\[
V = A \times \text{depth} = 115 \text{ ft}^2 \times 10 \text{ ft} = 1150 \text{ cubic feet}
\]
### Final Result
So, Samira's pool can hold **1150 cubic feet** of water. If other dimensions apply differently, update your height and repeat the calculations accordingly.
### Step 1: Find 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 (bases),
- \( h \) is the height (the distance between the two bases).
In this case, let's assume:
- \( b_1 = 5 \) ft (one of the parallel sides),
- \( b_2 = 18 \) ft (the other parallel side),
- The height \( h \) between the bases can be calculated using the side lengths \( 25 \) ft and \( 10 \) ft.
However, since we only need \( h \) to calculate the area, we use the following property: in a right trapezoid, the height can directly be the vertical distance between the two parallel sides.
Assuming the height can be determined from the right trapezoid, let's assume we've determined a height based on the geometry, here's an example with common trapezoidal dimensions.
### Step 2: Calculate the area using approximate height
We do not have the height directly specified. Assuming it should be calculated, for a right trapezoid, it is often the shorter base that acts similarly. For simplicity, we can use:
\[
h = 10 \text{ ft}
\]
Now calculate the area:
\[
A = \frac{1}{2} \times (5 + 18) \times 10
\]
Calculating this gives:
\[
A = \frac{1}{2} \times 23 \times 10 = \frac{230}{2} = 115 \text{ square feet}
\]
### Step 3: Find the volume of the prism
To find the volume \( V \) of the prism, we multiply the area of the trapezoidal base by the height of the prism. If we assume the height of the prism (the depth) is, for example, 10 ft:
\[
V = A \times \text{depth} = 115 \text{ ft}^2 \times 10 \text{ ft} = 1150 \text{ cubic feet}
\]
### Final Result
So, Samira's pool can hold **1150 cubic feet** of water. If other dimensions apply differently, update your height and repeat the calculations accordingly.