The school is building a circular fish pond in the courtyard. The diameter of the pond will be 10 feet. Around the pond will be a sidewalk that is 3 feet wide. What is the area of the sidewalk?
The school is building a circular fish pond in the courtyard. The diameter of the pond will be 10 feet. Around the pond will be a sidewalk that is 3 feet wide. What is the area of the sidewalk?
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Question
![**Problem Description:**
The school is building a circular fish pond in the courtyard. The diameter of the pond will be 10 feet. Around the pond will be a sidewalk that is 3 feet wide.
**Question:**
What is the area of the sidewalk?
**Solution Approach:**
1. **Calculate the Radius of the Pond:**
The diameter of the pond is given as 10 feet. The radius is half of the diameter.
\[
\text{Radius of the pond} = \frac{10}{2} = 5 \text{ feet}
\]
2. **Calculate the Radius of the Pond Plus Sidewalk:**
The sidewalk extends 3 feet beyond the pond. Thus, the radius of the pond plus the sidewalk is:
\[
\text{Radius of pond + sidewalk} = 5 + 3 = 8 \text{ feet}
\]
3. **Calculate the Area of the Pond:**
The formula for the area of a circle is \(\pi \times (\text{radius})^2\).
\[
\text{Area of the pond} = \pi \times (5)^2 = 25\pi \text{ square feet}
\]
4. **Calculate the Total Area of the Pond Plus Sidewalk:**
\[
\text{Total Area} = \pi \times (8)^2 = 64\pi \text{ square feet}
\]
5. **Calculate the Area of the Sidewalk:**
The area of the sidewalk is the total area minus the area of the pond.
\[
\text{Area of the sidewalk} = 64\pi - 25\pi = 39\pi \text{ square feet}
\]
Therefore, the area of the sidewalk is \(39\pi\) square feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fead4898a-5cbe-436c-8de1-efb4210c8ea9%2F8a0dded6-90fd-4c1d-aefe-f4ab88268862%2Fso2vtfu_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
The school is building a circular fish pond in the courtyard. The diameter of the pond will be 10 feet. Around the pond will be a sidewalk that is 3 feet wide.
**Question:**
What is the area of the sidewalk?
**Solution Approach:**
1. **Calculate the Radius of the Pond:**
The diameter of the pond is given as 10 feet. The radius is half of the diameter.
\[
\text{Radius of the pond} = \frac{10}{2} = 5 \text{ feet}
\]
2. **Calculate the Radius of the Pond Plus Sidewalk:**
The sidewalk extends 3 feet beyond the pond. Thus, the radius of the pond plus the sidewalk is:
\[
\text{Radius of pond + sidewalk} = 5 + 3 = 8 \text{ feet}
\]
3. **Calculate the Area of the Pond:**
The formula for the area of a circle is \(\pi \times (\text{radius})^2\).
\[
\text{Area of the pond} = \pi \times (5)^2 = 25\pi \text{ square feet}
\]
4. **Calculate the Total Area of the Pond Plus Sidewalk:**
\[
\text{Total Area} = \pi \times (8)^2 = 64\pi \text{ square feet}
\]
5. **Calculate the Area of the Sidewalk:**
The area of the sidewalk is the total area minus the area of the pond.
\[
\text{Area of the sidewalk} = 64\pi - 25\pi = 39\pi \text{ square feet}
\]
Therefore, the area of the sidewalk is \(39\pi\) square feet.
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