Question
Tim has a backyard pool in the shape of two semicircles attached to a square. Each side of the square measures 50 ft. Find the area of the pool. Use pialmost equals3.14.
50 ft.
Question content area bottom
Part 1
Tim's pool has an area of about
enter your response here square feet.
(Type an integer or decimal rounded to the nearest tenth as needed.)
50 ft.
Question content area bottom
Part 1
Tim's pool has an area of about
enter your response here square feet.
(Type an integer or decimal rounded to the nearest tenth as needed.)
Answers
GPT-4o mini
To find the area of Tim's pool, which consists of a square and two semicircles, we'll need to calculate the area separately for the square and the semicircles and then add them together.
1. **Area of the Square:**
The formula for the area of a square is given by:
\[
\text{Area}_{\text{square}} = \text{side}^2
\]
For Tim's pool, the side length of the square is 50 ft:
\[
\text{Area}_{\text{square}} = 50^2 = 2500 \, \text{ft}^2
\]
2. **Area of the Two Semicircles:**
The radius of each semicircle is half the side length of the square:
\[
\text{radius} = \frac{50}{2} = 25 \, \text{ft}
\]
The area of a full circle is given by:
\[
\text{Area}_{\text{circle}} = \pi r^2
\]
Therefore, the area of one semicircle is:
\[
\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (25^2) = \frac{1}{2} \pi (625) = 312.5 \pi
\]
Using \( \pi \approx 3.14 \):
\[
\text{Area}_{\text{semicircle}} \approx 312.5 \times 3.14 = 982.5 \, \text{ft}^2
\]
Since there are two semicircles, the total area of both semicircles is:
\[
\text{Area}_{\text{two semicircles}} = 2 \times 982.5 = 1965 \, \text{ft}^2
\]
3. **Total Area of the Pool:**
Now, we add the area of the square and the area of the two semicircles:
\[
\text{Total Area} = \text{Area}_{\text{square}} + \text{Area}_{\text{two semicircles}} = 2500 + 1965 = 4465 \, \text{ft}^2
\]
Thus, Tim's pool has an area of about **4465.0 square feet.**
1. **Area of the Square:**
The formula for the area of a square is given by:
\[
\text{Area}_{\text{square}} = \text{side}^2
\]
For Tim's pool, the side length of the square is 50 ft:
\[
\text{Area}_{\text{square}} = 50^2 = 2500 \, \text{ft}^2
\]
2. **Area of the Two Semicircles:**
The radius of each semicircle is half the side length of the square:
\[
\text{radius} = \frac{50}{2} = 25 \, \text{ft}
\]
The area of a full circle is given by:
\[
\text{Area}_{\text{circle}} = \pi r^2
\]
Therefore, the area of one semicircle is:
\[
\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (25^2) = \frac{1}{2} \pi (625) = 312.5 \pi
\]
Using \( \pi \approx 3.14 \):
\[
\text{Area}_{\text{semicircle}} \approx 312.5 \times 3.14 = 982.5 \, \text{ft}^2
\]
Since there are two semicircles, the total area of both semicircles is:
\[
\text{Area}_{\text{two semicircles}} = 2 \times 982.5 = 1965 \, \text{ft}^2
\]
3. **Total Area of the Pool:**
Now, we add the area of the square and the area of the two semicircles:
\[
\text{Total Area} = \text{Area}_{\text{square}} + \text{Area}_{\text{two semicircles}} = 2500 + 1965 = 4465 \, \text{ft}^2
\]
Thus, Tim's pool has an area of about **4465.0 square feet.**