1. An ice skater skates completely around the two circles shown in the diagram. Each circle has a diameter of 20 meters. 20 m 20 m What is the approximate total distance skated by the ice skater? A. 63 meters B. 126 meters ft C. 251 meters D. 628 meters
1. An ice skater skates completely around the two circles shown in the diagram. Each circle has a diameter of 20 meters. 20 m 20 m What is the approximate total distance skated by the ice skater? A. 63 meters B. 126 meters ft C. 251 meters D. 628 meters
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
- The top circle has a diameter of 20 meters, as indicated by a dashed horizontal line labeled "20 m".
- The bottom circle is identical, also with a diameter of 20 meters.
**Question:**
What is the approximate total distance skated by the ice skater?
**Options:**
- **A. 63 meters**
- **B. 126 meters**
- **C. 251 meters**
- **D. 628 meters**
**Explanation:**
To find the total distance skated by the ice skater around both circles, we need to calculate the circumference of each circle and add them together.
**Step-by-step Calculation:**
1. **Find the radius:**
\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{20 \text{ meters}}{2} = 10 \text{ meters}
\]
2. **Calculate the circumference of one circle:**
\[
\text{Circumference} = 2 \pi \times \text{Radius} = 2 \pi \times 10 \text{ meters} = 20 \pi \text{ meters}
\]
3. **Calculate the total circumference for two circles:**
\[
\text{Total Distance} = 2 \times 20 \pi \text{ meters} = 40 \pi \text{ meters}
\]
4. **Approximate using \(\pi \approx 3.14\):**
\[
40 \pi \approx 40 \times 3.14 = 125.6 \text{ meters}
\]
Thus, the approximate total distance skated by the ice skater is \( \boxed{126 \text{ meters}} \).
**Correct Option: B. 126 meters**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7acfa03c-ce8c-4cd5-a52f-d1ef747591d8%2F9518952f-80fe-497c-9cd9-df4b34549bea%2F9yi2248_processed.png&w=3840&q=75)
Transcribed Image Text:### Ice Skating Distance Calculation
**Problem Statement:**
1. An ice skater skates completely around the two circles shown in the diagram. Each circle has a diameter of 20 meters.
- The top circle has a diameter of 20 meters, as indicated by a dashed horizontal line labeled "20 m".
- The bottom circle is identical, also with a diameter of 20 meters.
**Question:**
What is the approximate total distance skated by the ice skater?
**Options:**
- **A. 63 meters**
- **B. 126 meters**
- **C. 251 meters**
- **D. 628 meters**
**Explanation:**
To find the total distance skated by the ice skater around both circles, we need to calculate the circumference of each circle and add them together.
**Step-by-step Calculation:**
1. **Find the radius:**
\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{20 \text{ meters}}{2} = 10 \text{ meters}
\]
2. **Calculate the circumference of one circle:**
\[
\text{Circumference} = 2 \pi \times \text{Radius} = 2 \pi \times 10 \text{ meters} = 20 \pi \text{ meters}
\]
3. **Calculate the total circumference for two circles:**
\[
\text{Total Distance} = 2 \times 20 \pi \text{ meters} = 40 \pi \text{ meters}
\]
4. **Approximate using \(\pi \approx 3.14\):**
\[
40 \pi \approx 40 \times 3.14 = 125.6 \text{ meters}
\]
Thus, the approximate total distance skated by the ice skater is \( \boxed{126 \text{ meters}} \).
**Correct Option: B. 126 meters**
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