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Fun with Arc Lengths: Unit 10 Circle Homework & Answers

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Fun with Arc Lengths: Unit 10 Circle Homework & Answers

Understanding arc length in u10l3 notes provides essential knowledge for calculating partial circumferences of circles. This guide covers the arc length formula, step-by-step examples, and practical applications.

  • Arc length formula: l = (x/360°) * C, where x is the central angle in degrees and C is the circumference
  • Examples demonstrate how to calculate arc lengths for various circle sizes and central angles
  • Applications include real-world scenarios like pendulum swings and roundabout travel distances
  • Practice problems reinforce understanding of arc length calculations in different contexts

2/7/2023

521

Name:
Topic:
Main Ideas/Questions
ARC LENGTH
r
1
Notes/Examples
Arc Length Formula:
1.
3.
x = degree measure of arc
C = circumference
(C= 2π

Arc Length Formula and Basic Examples

The first page introduces the fundamental concept of arc length and provides the essential formula for its calculation.

Definition: Arc length is a portion of the circumference of a circle.

The page presents the arc length formula:

Highlight: Arc Length = (x/360°) * C, where x is the degree measure of the arc and C is the circumference.

Several examples are provided to illustrate the application of this formula:

  1. For a circle with a radius of 6 meters and a central angle of 142°, the arc length is calculated to be approximately 14.85 meters.

  2. In a circle with a radius of 15 inches and a central angle of 288°, the arc length is found to be about 75.40 inches.

  3. For a circle with a diameter of 8 cm and a central angle of 107°, the arc length is calculated to be approximately 7.47 cm.

  4. In a circle with a radius of 9.5 feet and a central angle of 38°, the arc length is determined to be about 6.30 feet.

  5. Given that EB = 15 centimeters and the central angle is 112°, the length of arc CD is calculated to be approximately 29.32 cm.

  6. With NR = 8 feet and a central angle of 162°, the length of arc NMP is found to be about 22.61 feet.

These examples demonstrate how to apply the arc length formula in various scenarios, reinforcing the concept for students learning how to calculate arc lengths u10l3 step by step.

Name:
Topic:
Main Ideas/Questions
ARC LENGTH
r
1
Notes/Examples
Arc Length Formula:
1.
3.
x = degree measure of arc
C = circumference
(C= 2π

View

Applications of Arc Length

The second page focuses on applying the arc length formula to more complex problems and real-world scenarios. This section helps students understand how to find arc length with radius in practical situations.

  1. Given VS = 12 meters and a central angle of 53°, the length of arc UT is calculated to be approximately 11.10 meters.

  2. With JH = 21 inches and a central angle of 334°, the length of arc KJG is determined to be about 61.21 inches.

  3. For FG = 27 yards and a central angle of 233°, the length of arc FED is found to be approximately 109.8 yards.

  4. Given WS = 4.5 millimeters and a central angle of 280°, the length of arc TS is calculated to be about 7.62 millimeters.

  5. A practical application involving a pendulum is presented:

Example: A 16-inch pendulum swings through an angle of 40°. The tip of the pendulum travels approximately 11.17 inches in a single swing.

  1. Another real-world application involves a car traveling in a roundabout:

Example: A car enters a roundabout with a diameter of 150 feet, travels 280 feet, and exits. The angle of rotation is calculated to be approximately 214°.

These applications demonstrate the versatility of the arc length formula and its relevance in solving real-world problems, helping students understand how to find arc length in various contexts.

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SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Fun with Arc Lengths: Unit 10 Circle Homework & Answers

Understanding arc length in u10l3 notes provides essential knowledge for calculating partial circumferences of circles. This guide covers the arc length formula, step-by-step examples, and practical applications.

  • Arc length formula: l = (x/360°) * C, where x is the central angle in degrees and C is the circumference
  • Examples demonstrate how to calculate arc lengths for various circle sizes and central angles
  • Applications include real-world scenarios like pendulum swings and roundabout travel distances
  • Practice problems reinforce understanding of arc length calculations in different contexts

2/7/2023

521

 

Geometry

14

Name:
Topic:
Main Ideas/Questions
ARC LENGTH
r
1
Notes/Examples
Arc Length Formula:
1.
3.
x = degree measure of arc
C = circumference
(C= 2π

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Arc Length Formula and Basic Examples

The first page introduces the fundamental concept of arc length and provides the essential formula for its calculation.

Definition: Arc length is a portion of the circumference of a circle.

The page presents the arc length formula:

Highlight: Arc Length = (x/360°) * C, where x is the degree measure of the arc and C is the circumference.

Several examples are provided to illustrate the application of this formula:

  1. For a circle with a radius of 6 meters and a central angle of 142°, the arc length is calculated to be approximately 14.85 meters.

  2. In a circle with a radius of 15 inches and a central angle of 288°, the arc length is found to be about 75.40 inches.

  3. For a circle with a diameter of 8 cm and a central angle of 107°, the arc length is calculated to be approximately 7.47 cm.

  4. In a circle with a radius of 9.5 feet and a central angle of 38°, the arc length is determined to be about 6.30 feet.

  5. Given that EB = 15 centimeters and the central angle is 112°, the length of arc CD is calculated to be approximately 29.32 cm.

  6. With NR = 8 feet and a central angle of 162°, the length of arc NMP is found to be about 22.61 feet.

These examples demonstrate how to apply the arc length formula in various scenarios, reinforcing the concept for students learning how to calculate arc lengths u10l3 step by step.

Name:
Topic:
Main Ideas/Questions
ARC LENGTH
r
1
Notes/Examples
Arc Length Formula:
1.
3.
x = degree measure of arc
C = circumference
(C= 2π

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Applications of Arc Length

The second page focuses on applying the arc length formula to more complex problems and real-world scenarios. This section helps students understand how to find arc length with radius in practical situations.

  1. Given VS = 12 meters and a central angle of 53°, the length of arc UT is calculated to be approximately 11.10 meters.

  2. With JH = 21 inches and a central angle of 334°, the length of arc KJG is determined to be about 61.21 inches.

  3. For FG = 27 yards and a central angle of 233°, the length of arc FED is found to be approximately 109.8 yards.

  4. Given WS = 4.5 millimeters and a central angle of 280°, the length of arc TS is calculated to be about 7.62 millimeters.

  5. A practical application involving a pendulum is presented:

Example: A 16-inch pendulum swings through an angle of 40°. The tip of the pendulum travels approximately 11.17 inches in a single swing.

  1. Another real-world application involves a car traveling in a roundabout:

Example: A car enters a roundabout with a diameter of 150 feet, travels 280 feet, and exits. The angle of rotation is calculated to be approximately 214°.

These applications demonstrate the versatility of the arc length formula and its relevance in solving real-world problems, helping students understand how to find arc length in various contexts.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

13 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying