This is a self-learning module (SLM) for Grade 5 Mathematics, Quarter 3, Module 20: Finding the Circumference of a Circle. It was developed by DepEd Region VIII for home-based learning. It helps learners find a circle’s radius, diameter, and circumference and use these skills to solve real-life problems.
On this page 7 sections
What learners will learn
By the end of the module, learners are expected to:
- find the radius and diameter of a circle;
- find the circumference of a circle; and
- appreciate the value of knowing how to find the circumference of a circle in real-life situations.
Key ideas: parts of a circle
A circle is a closed plane figure. Unlike a polygon, it is not bounded by line segments. It is made up of points that are all the same distance from a fixed point called the center. To find the circumference, you only need the diameter or the radius.
| Term | Symbol | Meaning |
|---|---|---|
| Diameter | d | The distance between two points on the circle along a straight line through the center |
| Radius | r | The distance from the center to any point on the circle; half the diameter (r = ½ d) |
| Circumference | C | The distance around the circle |
Because the radius is half the diameter, the diameter is twice the radius (d = 2r). For example, a circle with a diameter of 14 cm has a radius of 7 cm.
Key ideas: where pi comes from and the formulas
The module starts with a hands-on investigation. Learners wrap a string around three circular cans of different sizes to measure their circumference. Then they measure each diameter with a ruler and divide the circumference by the diameter. The quotient is always about the same. This constant ratio, about 22/7 or 3.14, is called pi (π).
Since C ÷ d = π, multiplying both sides by d gives the circumference formula. The module uses π = 3.14.
| What you know | What you want | Formula |
|---|---|---|
| Diameter | Circumference | C = π x d |
| Radius | Circumference | C = 2 x π x r |
| Circumference | Diameter | d = C ÷ π |
| Circumference | Radius | r = C ÷ 2π |
Worked examples from the module
- Fencing a garden: Mrs. Violeta Banzon’s circular flower garden has a diameter of 8 meters. C = 3.14 x 8 = 25.12 m, so she needs 25.12 meters of fencing.
- Radius given: A circle with a radius of 12 cm has C = 2 x 3.14 x 12 = 75.36 cm.
- Finding the diameter: A circle with a circumference of 37.68 cm has d = 37.68 ÷ 3.14 = 12 cm.
- Finding the radius: A circle with a circumference of 23.55 cm has r = 23.55 ÷ 6.28 = 3.75 cm.
Parts and activities of the module
The module has one lesson, Finding the Circumference of a Circle, arranged in these parts:
- What I Know: a 10-item multiple-choice pretest.
- What’s In: a review of circle parts, the can investigation, and two drills. One drill finds the radius or diameter, and the other picks the correct formula.
- What’s New: the circumference formulas and how to get the diameter and radius from them.
- What is It: the worked examples above.
- What’s More: three exercises. In “Let’s C!” learners find circumferences. In “C-Saw” they fill in radius, diameter, and circumference from drawings. In “The Circle of Life” they draw circles with a compass and ruler and find their circumference.
- What I Have Learned: learners write the two formulas and compare a garden with a 62.8 m circumference to a room with a 19 m diameter.
- What I Can Do: real-life problems about a round farmhouse table with a 92.8 cm radius and a tablecloth with a 15 cm allowance.
- Assessment: a 10-item multiple-choice post-test.
- Additional Activities: five more circles to solve.
How to use this module
- Learners: Take the pretest first. If you score 9 or 10, you should have no trouble with the lesson. If you score 8 or below, study the lesson carefully and do all the activities. Write your answers on a separate sheet, not on the module, and check your work honestly against the answer key. After the post-test, a score of 8 to 10 means you are ready for the next module. A lower score means you should go over the lesson and exercises again.
- Parents and facilitators: For the investigation, prepare three circular cans of different sizes, a string, and a ruler. A compass and ruler are needed for “The Circle of Life.” The module includes Notes to the Teacher with tips for helping at home.
- Teachers: The answer key is on the last page of the module, although the module’s text points to page 11. Review the key before handing it to learners, because a few entries do not match the printed items.
Frequently asked questions
What grade and quarter is this circumference module for?
It is for Grade 5 Mathematics, Quarter 3. It is Module 20, titled Finding the Circumference of a Circle.
What is the formula for the circumference of a circle?
If the diameter is given, use C = π x d. If the radius is given, use C = 2 x π x r. The module uses π = 3.14.
How do I find the radius or diameter if I only know the circumference?
Divide the circumference by π to get the diameter (d = C ÷ π). Divide it by 2π to get the radius (r = C ÷ 2π).
Does the module have an answer key?
Yes. It has answers for the pretest, activities, post-test, and additional activities, printed on the last page of the module.
What materials are needed for the activities?
The investigative activity uses three circular cans of different sizes, a string, and a ruler. The Circle of Life activity needs a compass and a ruler.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 3 – Module 20: Finding the Circumference of a Circle
CO_Q3_Mathematics 5_ Module 20
Mathematics
Quarter 3 – Module 20: Finding the Circumference of a Circle
5
[illustration: students reading and studying outdoors under a tree and at a table with a teacher, a globe, and a child working by a lamp]
GOVERNMENT PROPERTY NOT FOR SALE
Mathematics – Grade 5 Alternative Delivery Mode Quarter 3 – Module 20: Finding the Circumference of a Circle First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Development Team of the Module
Writers: Fe C. Cruz Editors: Jose J. Sagada Jr. Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim, Teodora P. Coreal. Rodel V. Rosales Illustrator: – Layout Artist: Joey Sustitudo, Jaycee B. Barcelona Management Team: Ma. Gemma M. Ledesma, Arnulfo R. Balane, Rosemarie M. Guino, Joy B. Bihag, Ryan R. Tiu, Sarah S. Cabaluna, Thelma Cabadsan-Quitalig, Elena S. De Luna, Renato S. Cagomoc, Noel E. Sagayap, Geraldine P. Sumbise, Joshua Sherwin T. Lim
Printed in the Philippines by ________________________
Department of Education – Region VIII
Office Address: DepEd Regional Office No. 8, Candahug, Palo, Leyte Telefax: (053)-832- 2997 E-mail Address: region8@deped.gpv.ph
5
Mathematics
Quarter 3 – Module 20: Finding the Circumference of a Circle
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
Hello there, Mathletes! As you know, a circle is a plane figure that is commonly used in art, design, architecture, manufacturing, engineering, and many others. In fact, the coins in your purse are circular in shape! In this module, you will learn how to find the circumference of a circle. Your ability to learn the concepts and keep up with the tasks will depend to a large extent on your willingness to learn. So, are you ready?
At the end of this module, you are expected to:
- find the radius and diameter of a circle;
- find the circumference of a circle; and
- appreciate the value of knowing how to find the circumference of a circle in real-life situations.
What I Know
Directions: Read each statement carefully. Choose the letter that corresponds to the best answer. Write your answer on a separate sheet of paper.
If the diameter of a circle is 14 cm, how long is the radius?
- A. 6 cm B. 7 cm C. 14 cm D. 28 cm
Which of the following is the formula in finding the circumference of a circle if the radius is given?
- A. C = π x d B. C = r x d C. C = π x r D. C = 2 x π x r
If a circle’s radius measures 15 cm, what is its diameter?
- A. 30 cm B. 15 m C. 17 cm D. 7.5 cm
Rolly receives a gold medal whose diameter is 15 cm. Which of the following expressions will give the circumference of the medal?
- A. 3.14 x 7.5 B. 3.14 x 1.5 C. 3.14 x 15 D. 3.14 + 15
If the radius is doubled, what happens to the diameter of the circle?
- A. The diameter is also doubled.
- B. The diameter remains the same.
- C. The diameter is increased by 2.
- D. The diameter will be the same as the radius.
The circular pond has a diameter of 7 meters. What is the circumference of the pond to the nearest meter? Use π = 3.14.
- A. 14 B. 17 C. 20 D. 22
Marlon’s bicycle wheel has a diameter of 40 cm. What is the circumference of the wheel?
- A. 120.40 cm B. 121.12 cm C. 122.05 cm D. 125.60 cm
Myrna’s circular garden is 10 meters in diameter. How many meters of wire are needed to put a fence around it? Use π=3.14.
- A. 25.50 m B. 30.10 m C. 31.40 m D. 32.50 m
Mr. Corsiga is laying out a circular garden whose circumference is 251.20 meters. What is its radius? Use π=3.14.
- A. 40 m B. 50 m C. 125 m D. 250 m
Using π=3.14, find the circumference of the circle:
[illustration: circle with a radius line labeled 11cm]
- A. 70.28 cm B. 69.08 cm C. 67.02 cm D. 66.12 cm
Please check your answers against the answer key on page 11.
CONGRATULATIONS! If you got a score of 9 or 10, you should not have any difficulty studying the lesson in this module.
If you got a score of 8 or below, you may need to study the lesson more carefully and do all the given activities.
[illustration: smiling boy character in a box with the congratulations message]
[transcriber’s note: the source text layer of this page also contains the line “if you got 8 or lower, you”, which is not visible in the rendered page and was omitted]
Lesson 1 Finding the Circumference of a Circle
To find the circumference of a circle, it is important to identify its diameter or radius. Deriving the formula for getting the circumference of a circle is also very helpful for you to understand how the formula was arrived at.
What’s In
Before we take the challenges ahead, let’s first look back at the wonderful world of circles.
A circle is a closed plane figure, but unlike a polygon, it is not bounded by line segments. It is made up of points which are equidistant from a fixed point called the center. A circle has many parts. In finding the circumference of a circle, we only need the measure of its diameter or radius.
Diameter, denoted by d, is the distance between two points on a circle which form a straight line passing through its center.
Radius, denoted by r, is the distance from the center to any point on the circle. The radius is half the length of the diameter. (r = ½ d)
Circumference, denoted by C, is the distance around the circle.
INVESTIGATIVE ACTIVITY
Let us explore the ratio between a circle’s circumference and diameter through this activity.
- Measure the circumference of three circular cans of different sizes by wrapping a string around each can and measuring the length of the string at the point where it overlaps.
- Measure the diameter of the can using a ruler.
- Divide the circumference of each can by its diameter.
- Tabulate the results for the 3 cans.
| Can | Circumference | Diameter | C/d |
|---|---|---|---|
| A | |||
| B | |||
| C |
What do you observe about the quotient of the circumference and diameter?
The ratio of any circle’s circumference to its diameter is constant, and that is about 22/7, or 3.14. This ratio is represented by the Greek letter π (pi). Using the ratio, you can write the formula in finding the circumference of a circle.
The investigative activity above showed that C/d = π, where C is the circumference and d is the diameter of the circle. By multiplying both sides of the equation by d, we get C = π x d. Thus, to find the circumference of a circle:
a. If the diameter is given, multiply the diameter by π. Use π = 3.14. C = π x d
b. If the radius is given, multiply π by twice the radius. Use π = 3.14. C = 2r x π or C = 2 x π x r
Here’s a simple drill for you.
Activity 1
Directions: Each item refers to the same circle. Find the diameter of the circle when its radius is given. Find the radius of the circle when the diameter is given.
| Radius | Diameter |
|---|---|
| 1. 6 inches | ____________________ |
| 2. ____________________ | 22 m |
| 3. 15 mm | ____________________ |
| 4. ____________________ | 18 km |
| 5. 22.5 cm | ____________________ |
Activity 2
Directions: Complete the table. Given the following, write the correct formula in finding the circumference of the circle. The first one has been done for you.
| Given | Formula |
|---|---|
| 1. r = 5 in | C = 2 x π x r |
| 2. d = 3 m | |
| 3. r = 10 mm | |
| 4. r = 15 dm | |
| 5. d = 7 m |
What’s New
Two formulas are used to find the circumference (denoted by C) of a circle, depending on the given information.
Formulas for Finding the Circumference of a Circle
- If the diameter is given:
C = π x d - If the radius is given:
C = π x 2r
or
C = 2 x π x r
since the value of diameter is twice the radius; d = 2r
where C = circumference d = diameter r = radius π = 3.14
Given the formula in finding the circumference of the circle, you can also derive the following formulas:
- To find the diameter of the circle, divide the circumference by π (3.14). Hence;
d = C/π - To find the radius of the circle, divide the circumference by 2 π. Hence,
r = C/2π
What is It
Consider the situation:
Mrs. Violeta Banzon plants roses in her circular flower garden whose diameter is 8 meters. She wants to build a fence around the garden to protect her roses. How long will the fence be?
Can you help her solve this problem?
Since the diameter of the circular flower garden is 8 meters, we use the formula when the diameter is given. So,
C = π x d Given: d = 8 m Find: C? Solution: C = π x d = 3.14 x 8 = 25.12 m
Therefore, Mrs. Banzon needs 25.12 meters of fencing materials.
Let’s have more examples.
Example 1:
What is the circumference of the circle whose radius is 12 centimeters?
[illustration: circle with radius labeled 12 cm]
Since the radius of the circle is given, we use the formula below: C = 2 x π x r So: Given: r = 12 cm Find: C? Solution: C = 2 x π x r = 2 x 3.14 x 12 = 75.36 cm
Therefore, the circumference of the circle is 75.36 centimeters.
Example 2:
What is the diameter of a circle whose circumference is 37.68 centimeters?
Since the circumference of the circle is given and we are going to find its diameter, we use the formula below: d = C/π So: Given: C = 37.68 cm Find: d? Solution: d = C/π = 37.68 / 3.14 = 12 cm
Therefore, the diameter of the circle is 12 centimeters.
Example 3:
If the circumference of a circle is 23.55 cm, what is its radius?
Since the circumference of the circle is given and we are going to find its radius, we use the formula below: r = C/2π So: Given: C = 23.55 cm Find: r? Solution: r = C/2π = 23.55 / (2 x 3.14) = 23.55 / 6.28 = 3.75 cm
Therefore, the radius of the circle is 3.75 cm.
Are you now excited to use your knowledge of finding the circumference of a circle to answer the exercises in this module?
What’s More
This time, you will answer some exercises to check your ability in finding the circumference of the circle. Just relax and refer to the previous examples as your guide.
Activity 1: Let’s C!
Directions: Find the circumference of the circle given its radius or diameter. You can use an extra sheet for your solution.
- r = 2 m
C = ______ - d = 16 cm
C = ______ - d = 18 dm
C = ______ - r = 8 cm
C = ______ - r = 15 km
C = ______
Activity 2: C – Saw
Directions: Fill in the needed information based on the given illustration. The first one has been done for you.
| 1. | 2. | 3. |
|---|---|---|
| [illustration: circle with radius labeled 5 cm] | [illustration: circle with diameter labeled 8 m] | [illustration: circle with a line labeled 25 cm] |
| Radius: 5 cm | Radius: | Radius: |
| Diameter: 10 cm | Diameter: | Diameter: |
| Circumference: 31.4 cm | Circumference: | Circumference : |
Activity 3: The Circle of Life
Directions: Draw a circle with the given radius or diameter using a compass and ruler and find its circumference.
- d = 9 cm
- r = 18 mm
- r = 7 cm
- d = 28 cm
- d = 30 m
What I Have Learned
Let’s check what you have learned by answering the following questions.
What is the formula in finding the circumference of a circle given the following:
a. Diameter? _______________________________
b. Radius? _______________________________Which one is wider: a garden whose circumference is 62.8 meters or a room with a diameter of 19 meters? Why?
Complete the statement below.
In this lesson, aside from finding the circumference of a circle, I also learned that _____________________________________________________________
_____________________________________________________________.
What I Can Do
Circles are present everywhere. Day in and day out, we are in close encounter with these figures.
Let’s see if you can solve the following real-life problems:
- The round table in a farm house has a radius of 92.8 cm. Find the distance around the table.
- You want to make a beautiful tablecloth for the round table in (1). It has an allowance of 15 cm from the edge. What is the circumference of the tablecloth?
See, you have made it this far! Give yourself a hug for keeping up with the challenges in this module. Always keep up the good work.
Assessment
Directions: Read each statement carefully. Choose the letter that best corresponds to the correct answer. Write it on your answer sheet.
- Which of the following is the formula in finding the circumference of a circle if the diameter is given?
a. C = 2 x π x r
b. C = π x d
c. C = π x r
d. C = r x d - If the diameter of a circle is 15 meters, then what is the radius?
a. 7 m
b. 7.5 m
c. 8.5 m
d. 30 m - If the radius of a circle is 12.3 cm, then what is its diameter?
a. 20.8 cm
b. 21.20 cm
c. 23.40 cm
d. 24.6 cm - Find the circumference of a plate to the nearest inch with a diameter of 8 in.
a. 8
b. 16
c. 20
d. 25 - Danilo is jogging on a circular track with a circumference of 501.40 ft. Find the radius of the track to the nearest foot.
a. 80
b. 120
c. 250
d. 500 - The radius of a basin is 9.2 in. What is the circumference to the nearest inch?
a. 58
b. 59
c. 60
d. 90 - A wheel has a diameter of 9 meters. What is the circumference of the wheel?
a. 27.35 m
b. 28.26 m
c. 29.15 m
d. 26.12 m - Mr. Delos Santos had a circular lagoon. The distance across the lagoon passing through the center is 25 meters. What is the distance around it?
a. 77.3 m
b. 76.2 m
c. 78.5 m
d. 75.1 - What is the circumference of a circular table with a diameter of 14 meters?
a. 40.75 m
b. 42.12 m
c. 43.96 m
d. 44.15 m - Using π = 3.14, find the circumference of the circle. [illustration: circle labeled 13 dm]
a. 40.82 dm
b. 41.20 dm
c. 42.13 dm
d. 43.4 dm
Please check your answers with the ANSWER KEY on page 11.
Got a score of 8-10? CONGRATULATIONS! Job well done. See you in the next module. If below 8, you may have to go over the lessons and the exercises again.
Additional Activities
Directions: Find the circumference of each circle. Use 3.14 for the value of π. (Note: Circles not drawn to scale.)
- [illustration: circle with radius labeled 12 cm]
- [illustration: circle with diameter labeled 9 dm]
- [illustration: circle with radius labeled 5.5 cm]
- [illustration: circle with diameter labeled 17 m]
- [illustration: circle with radius labeled 6.3 m]
Answer Key
[transcriber’s note: this page is printed upside down; it is transcribed in reading order with the sections in their upright order]
What I Know
- B
- D
- A
- C
- A
- D
- D
- C
- A
- B
What’s In
Activity 1
- 12 in
- 11 m
- 30 mm
- 9 km
- 45 cm
Activity 2
- C = 2 x π x r
- C = π x d
- C = 2 x π x r
- C = 2 x π x r
- C = π x d
What’s More
Activity 1
- 12.56 m
- 50.24 cm
- 56.52 dm
- 50.24 cm
- 94.2 km
Activity 2: C – Saw
| Radius: 25 cm | Radius: 4 m | Radius: 5 in |
|---|---|---|
| Diameter: 50 cm | Diameter: 8 m | Diameter: 10 in |
| Circumference: 157 cm | Circumference: 25.12 m | Circumference: 31.4 in |
Activity 3: The Circle of Life
| 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
| [illustration: circle with diameter line] | [illustration: circle with radius line] | [illustration: circle with radius line] | [illustration: circle with diameter line] | [illustration: circle with diameter line] |
| d = 9 cm C = 28.26 cm | r = 18 mm C = 113.40 cm | r = 12 cm C = 75.36 m | d = 28 cm C = 87.92 cm | d = 30 m C = 94.2 m |
What I Have Learned
- a. C = π x d
b. C = 2 x π x r - Garden whose circumference is 62.8 meters or Room with a diameter of 19 meters?
Solution:
C = π x d
= 3.14 x 19 m
= 59.66 m
Therefore, the garden whose circumference is 62.8 meters is wider than the room with a diameter of 19 meters because its circumference is greater than the circumference of the room by 3.14 meters. - Answers may vary.
What I Can Do
- C = 582.784 cm
- C = 676.984 cm
Assessment
| 1. | B | 6. | A |
|---|---|---|---|
| 2. | B | 7. | B |
| 3. | D | 8. | C |
| 4. | D | 9. | C |
| 5. | A | 10. | A |
Additional Activities
- 75.36 in
- 28.26 dm
- 34.54 cm
- 53.38 m
- 39.564 m
References
De Leon Jr., A. (1998). Today’s Math (3rd Ed). Sibs Publishing House, Inc.
Lumbre, A. P. and Alvin C. & Ursua, A. (2016). 21st Century Mathletes 5 Textbook. Vibal Group, Inc.
Banao, M. & Barron, A. (2007) Building New Horizon in MATH. A Simplified Approach Worktext 5. St. Augustine Publications, Inc.
Mathematics I Textbook, SEDP Series
Burns, W. PRE-GED Mathematics, Steck-Vaughn Company, P.O. Box 26015, Austin, Texas 78755
For inquiries or feedback, please write or call:
Department of Education – Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
Leave a Reply