arc length lesson
pdf
keyboard_arrow_up
School
University of South Carolina *
*We aren’t endorsed by this school
Course
B221
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
9
Uploaded by DeanFireBoar49
3/17/24, 1
:
00 PM
Lesson Activity: Area of a Sector
Page 1 of 9
https://app.edmentum.com/content-delivery/lessonactivity/42bd02dd-12d2-4571-836f-df18868c046c/
?
bucketType=2&includeExplain=true
Lesson Activity
Arc length and Sector Area
This activity will help you meet these educational goals:
You will apply proportional relationships to solve problems involving arc length, area
of a sector, and radian measure.
Directions
Read the instructions for this self-checked activity. Submit your response to each
question, and check your answers. At the end of the activity, write a brief evaluation
of your work.
Activity
An architectural firm has been asked to submit a design for a new speedway. The
design must include the distance around the proposed track, where the distance is
measured along the boundary surrounding the infield. The firm has developed the
design shown in the diagram. Each length unit on the diagram represents one-tenth
of a mile.
Use this situation to answer the questions in this activity.
Part A
3/17/24, 1
:
00 PM
Lesson Activity: Area of a Sector
Page 2 of 9
https://app.edmentum.com/content-delivery/lessonactivity/42bd02dd-12d2-4571-836f-df18868c046c/
?
bucketType=2&includeExplain=true
Question 1
What is the length of the track, in miles, around turn A? Round your answer to three
decimal places.
Answer:
the length is about 0.471
Space used (includes formatting): 38 / 15000
Substitute the arc measure and radius for turn A into the arc length formula and
solve for the arc length.
Since all lengths on the diagram represent one-tenth of a mile, dividing the arc length
by 10 represents the length in miles.
The length the curve around turn A is approximately 0.471 miles.
Hide Sample Answer
Question 2
3/17/24, 1
:
00 PM
Lesson Activity: Area of a Sector
Page 3 of 9
https://app.edmentum.com/content-delivery/lessonactivity/42bd02dd-12d2-4571-836f-df18868c046c/
?
bucketType=2&includeExplain=true
Turn B has a sector area of . What is the measure of the central angle for turn B?
Type the correct answer in the box. Use numerals instead of words. If necessary, use
/ for the fraction bar.
Correct!
Explanation:
Substitute the area of the sector and radius at turn B into the area of a sector
formula and solve for the central angle measure.
So, the measure of the central angle,
, is
.
Question
102
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
3/17/24, 1
:
00 PM
Lesson Activity: Area of a Sector
Page 4 of 9
https://app.edmentum.com/content-delivery/lessonactivity/42bd02dd-12d2-4571-836f-df18868c046c/
?
bucketType=2&includeExplain=true
Question 3
Use the value of the central angle you found in question 2 and determine the length,
in miles, of the track around turn B. Round your answer to three decimal places.
Answer:
0.534 arc length = measure of arc , 360 degress x 2(pi)radius
Space used (includes formatting): 74 / 15000
Substitute the arc measure, or central angle measure, and radius for turn B into the
arc length formula and solve for the arc length.
Since all lengths on the diagram represent one-tenth of a mile, dividing the arc length
by 10 shows that the length of the track around turn B is about 0.534 miles.
Hide Sample Answer
Question 4
3/17/24, 1
:
00 PM
Lesson Activity: Area of a Sector
Page 5 of 9
https://app.edmentum.com/content-delivery/lessonactivity/42bd02dd-12d2-4571-836f-df18868c046c/
?
bucketType=2&includeExplain=true
The arc length of turn C is . What is the radian measure of the central angle of turn
C?
Select the correct answer.
Correct!
Explanation:
The radian measure of the central angle is the ratio of the arc length to the
radius. Since both these values are known, find their ratio.
So, the radian measure of the central angle for turn C is .
Question
3/17/24, 1
:
00 PM
Lesson Activity: Area of a Sector
Page 6 of 9
https://app.edmentum.com/content-delivery/lessonactivity/42bd02dd-12d2-4571-836f-df18868c046c/
?
bucketType=2&includeExplain=true
Question 5
Use the measurements you found in part A, questions 1-4 to find the total distance
around the track, in miles. Complete the table with the correct measurements.
Remember that each length unit on the diagram represents one-tenth of a mile.
Answer:
Length of Actual Speedway Track in Miles
Turn
A
Turn A to
Turn B
Turn
B
Turn B to
Turn C
Turn C
Turn C to
Turn A
Total
Length
0.471
0.5
0.534
0.8
0.723
miles
0.6
3.628
Space used (includes formatting): 1965 / 15000
Length of Actual Speedway Track in Miles
Turn A
Turn A to
Turn B
Turn B
Turn B to
Turn C
Turn C
Turn C to
Turn A
Total
Length
0.471
miles
0.5 miles
0.534
miles
0.8 miles
0.723
miles
0.6 miles
3.628
miles
So, the length of the actual speedway track will be about 3.6 miles.
Hide Sample Answer
Part B
The architectural firm designs the track so that the shaded, curved areas in the infield
will be viewing sections for the audience as shown. Each length unit in the diagram
represents one-tenth of a mile.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
3/17/24, 1
:
00 PM
Lesson Activity: Area of a Sector
Page 7 of 9
https://app.edmentum.com/content-delivery/lessonactivity/42bd02dd-12d2-4571-836f-df18868c046c/
?
bucketType=2&includeExplain=true
Question 1
Explain how to find the area of the viewing sections in the infield.
Answer:
To find the area of the infield viewing sections, one needs to identify the shape of the section and
then
apply the appropriate formula based on that shape. If the infield viewing section is rectangular,
you would
employ the formula for the area of a rectangle, which is length multiplied by width.
Space used (includes formatting): 326 / 15000
Each of the three viewing sections in the infield represent a sector of a circle. To find
the area of each of these sections, substitute in the values of the central angle
Hide Sample Answer
3/17/24, 1
:
00 PM
Lesson Activity: Area of a Sector
Page 8 of 9
https://app.edmentum.com/content-delivery/lessonactivity/42bd02dd-12d2-4571-836f-df18868c046c/
?
bucketType=2&includeExplain=true
measure and radius into the sector area formula. Then, find the sum of the three
areas. The final value will be divided by ten since each length unit in the diagram is
one-tenth of a mile.
Question 2
Determine the total area around the track. Round lengths in miles to three decimal
places.
Answer:
Area of Viewing Sections, in Miles
Sector A
Sector B
Sector C
Total Area
0.707
0.801 miles
1.084
2.592
Space used (includes formatting): 1211 / 15000
Area of Viewing Sections, in Miles
Sector A
Sector B
Sector C
Total Area
0.707 miles
0.801 miles
1.084 miles
2.592 miles
So, the viewing sections take up an area of about 2.6 miles.
Hide Sample Answer
Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score.
Then, write a brief evaluation of your work below. Note what you learned and what
challenged you.
3/17/24, 1
:
00 PM
Lesson Activity: Area of a Sector
Page 9 of 9
https://app.edmentum.com/content-delivery/lessonactivity/42bd02dd-12d2-4571-836f-df18868c046c/
?
bucketType=2&includeExplain=true
Answer:
4-5 i think i did pretty well
Space used (includes formatting): 36 / 15000
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help