Question
You want to install a 1 yd wide walk around a circular swimming pool. The diameter of the pool is 18 yd. What is the area of the walk? Use 3.14 for pi.
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Question content area top right
Part 1
18 yd
1 yd
Question content area bottom
Part 1
The area of the walk is approximately
enter your response here
▼
yd squared .
yd.
yd cubed .
(Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth as needed.)
.
.
.
Question content area top right
Part 1
18 yd
1 yd
Question content area bottom
Part 1
The area of the walk is approximately
enter your response here
▼
yd squared .
yd.
yd cubed .
(Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth as needed.)
Answers
GPT-4o mini
To find the area of the walk around the circular swimming pool, we need to calculate the area of the larger circle that includes both the pool and the walk, and then subtract the area of the pool itself.
1. **Calculate the radius of the pool:**
- The diameter of the pool is 18 yards, so the radius \( r \) of the pool is:
\[
r = \frac{diameter}{2} = \frac{18 \text{ yd}}{2} = 9 \text{ yd}
\]
2. **Calculate the radius of the larger circle (pool plus walk):**
- The walk is 1 yard wide, so the radius of the larger circle is:
\[
R = r + 1 \text{ yd} = 9 \text{ yd} + 1 \text{ yd} = 10 \text{ yd}
\]
3. **Calculate the area of the larger circle (pool plus walk):**
- The area \( A_{large} \) of a circle is given by the formula \( A = \pi R^2 \):
\[
A_{large} = 3.14 \times (10 \text{ yd})^2 = 3.14 \times 100 \text{ yd}^2 = 314 \text{ yd}^2
\]
4. **Calculate the area of the pool:**
- The area \( A_{small} \) of the pool can be calculated similarly:
\[
A_{small} = 3.14 \times (9 \text{ yd})^2 = 3.14 \times 81 \text{ yd}^2 = 254.34 \text{ yd}^2
\]
5. **Calculate the area of the walk:**
- The area of the walk, \( A_{walk} \), is the difference between the area of the larger circle and the area of the pool:
\[
A_{walk} = A_{large} - A_{small} = 314 \text{ yd}^2 - 254.34 \text{ yd}^2 = 59.66 \text{ yd}^2
\]
Rounding to the nearest hundredth, the area of the walk is approximately:
\[
\boxed{59.66} \text{ yd}^2
\]
1. **Calculate the radius of the pool:**
- The diameter of the pool is 18 yards, so the radius \( r \) of the pool is:
\[
r = \frac{diameter}{2} = \frac{18 \text{ yd}}{2} = 9 \text{ yd}
\]
2. **Calculate the radius of the larger circle (pool plus walk):**
- The walk is 1 yard wide, so the radius of the larger circle is:
\[
R = r + 1 \text{ yd} = 9 \text{ yd} + 1 \text{ yd} = 10 \text{ yd}
\]
3. **Calculate the area of the larger circle (pool plus walk):**
- The area \( A_{large} \) of a circle is given by the formula \( A = \pi R^2 \):
\[
A_{large} = 3.14 \times (10 \text{ yd})^2 = 3.14 \times 100 \text{ yd}^2 = 314 \text{ yd}^2
\]
4. **Calculate the area of the pool:**
- The area \( A_{small} \) of the pool can be calculated similarly:
\[
A_{small} = 3.14 \times (9 \text{ yd})^2 = 3.14 \times 81 \text{ yd}^2 = 254.34 \text{ yd}^2
\]
5. **Calculate the area of the walk:**
- The area of the walk, \( A_{walk} \), is the difference between the area of the larger circle and the area of the pool:
\[
A_{walk} = A_{large} - A_{small} = 314 \text{ yd}^2 - 254.34 \text{ yd}^2 = 59.66 \text{ yd}^2
\]
Rounding to the nearest hundredth, the area of the walk is approximately:
\[
\boxed{59.66} \text{ yd}^2
\]