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
Related questions
Question
![### Problem 21: Calculating the Circumference and Area of a Circle
**Question:**
What is the circumference and the area of the circle? Round to the nearest tenth.
**Given Data:**
- Radius (r) of the circle: 15 inches
**Figure:**
A simple illustration of a circle with a radius of 15 inches is depicted.
**Steps to Solve:**
1. **Formula for Circumference:**
\[
\text{Circumference} = 2 \pi r
\]
Plug in the radius:
\[
\text{Circumference} = 2 \pi \cdot 15
\]
2. **Formula for Area:**
\[
\text{Area} = \pi r^2
\]
Plug in the radius:
\[
\text{Area} = \pi \cdot (15)^2
\]
3. **Simplify and Calculate:**
**Circumference Calculation:**
\[
\text{Circumference} = 2 \cdot \pi \cdot 15 \approx 2 \cdot 3.14 \cdot 15 \approx 94.2 \text{ inches}
\]
**Area Calculation:**
\[
\text{Area} = \pi \cdot 225 \approx 3.14 \cdot 225 = 706.5 \text{ in}^2
\]
**Answer:**
- **Circumference:** 94.2 inches
- **Area:** 706.5 square inches
**Work:**
A detailed segment is provided for the work area, encouraging students to manually check and validate each step of their calculations.
**Result:**
- **Circumference:** [Blank box for student's input]
- **Area:** [Blank box for student's input]
### Diagram Explanation:
An image appears showing a circle with a radius of 15 inches labeled. The image also includes placeholder areas for detailed "Work", leading to final boxed areas for "Circumference" and "Area" where students can fill in their answers after completing the calculations.
This problem encourages the application of formulas for circumference and area of a circle, reinforcing the understanding of geometric principles and mathematical computations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2f7ec59-fa10-41c8-b515-177e0c568bb4%2F1b3b5727-454c-4513-aca7-0e6a625a783d%2Fv2l2mlb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 21: Calculating the Circumference and Area of a Circle
**Question:**
What is the circumference and the area of the circle? Round to the nearest tenth.
**Given Data:**
- Radius (r) of the circle: 15 inches
**Figure:**
A simple illustration of a circle with a radius of 15 inches is depicted.
**Steps to Solve:**
1. **Formula for Circumference:**
\[
\text{Circumference} = 2 \pi r
\]
Plug in the radius:
\[
\text{Circumference} = 2 \pi \cdot 15
\]
2. **Formula for Area:**
\[
\text{Area} = \pi r^2
\]
Plug in the radius:
\[
\text{Area} = \pi \cdot (15)^2
\]
3. **Simplify and Calculate:**
**Circumference Calculation:**
\[
\text{Circumference} = 2 \cdot \pi \cdot 15 \approx 2 \cdot 3.14 \cdot 15 \approx 94.2 \text{ inches}
\]
**Area Calculation:**
\[
\text{Area} = \pi \cdot 225 \approx 3.14 \cdot 225 = 706.5 \text{ in}^2
\]
**Answer:**
- **Circumference:** 94.2 inches
- **Area:** 706.5 square inches
**Work:**
A detailed segment is provided for the work area, encouraging students to manually check and validate each step of their calculations.
**Result:**
- **Circumference:** [Blank box for student's input]
- **Area:** [Blank box for student's input]
### Diagram Explanation:
An image appears showing a circle with a radius of 15 inches labeled. The image also includes placeholder areas for detailed "Work", leading to final boxed areas for "Circumference" and "Area" where students can fill in their answers after completing the calculations.
This problem encourages the application of formulas for circumference and area of a circle, reinforcing the understanding of geometric principles and mathematical computations.
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