Lesson 1 Homework Practice: Circumference

In this lesson, you will learn how to calculate the circumference of a circle, which is the distance around the edge of the circle. You will also learn how to use the formulas for circumference in different situations. You will need a calculator and a ruler for this lesson.

What is the circumference of a circle?

The circumference of a circle is the linear distance of a circle’s edge. It is similar to the perimeter of a polygon, but the term perimeter is used only for shapes with straight sides. The circumference of a circle depends on its diameter or radius, which are measurements of the circle’s size.

What are the formulas for circumference?

There are two main formulas for finding the circumference of a circle, depending on whether you know the diameter or the radius of the circle. The diameter is the longest distance across the circle, passing through the center. The radius is half of the diameter, or the distance from the center to any point on the edge. The formulas are:

  • C = πd, where C is the circumference and d is the diameter.
  • C = 2πr, where C is the circumference and r is the radius.

In both formulas, π (pi) is a constant that is approximately equal to 3.14 or 22/7. It is an irrational number, which means it cannot be written as a fraction or a decimal with a finite number of digits. You can use your calculator to find its numerical value.

How to find the circumference of a circle using the diameter?

If you know the diameter of a circle, you can use the formula C = πd to find its circumference. Here are the steps:

  1. Measure or find out the diameter of the circle.
  2. Plug the value of the diameter into the formula and multiply it by π.
  3. Round your answer to an appropriate level of accuracy.

For example, suppose you have a circular plate with a diameter of 10 inches. To find its circumference, you can follow these steps:

  1. The diameter of the plate is 10 inches.
  2. C = πd = π x 10 = 31.4 inches.
  3. Rounding to one decimal place, the circumference is 31.4 inches.

How to find the circumference of a circle using the radius?

If you know the radius of a circle, you can use the formula C = 2πr to find its circumference. Here are the steps:

  1. Measure or find out the radius of the circle.
  2. Plug the value of the radius into the formula and multiply it by 2π.
  3. Round your answer to an appropriate level of accuracy.

For example, suppose you have a circular cookie with a radius of 3 inches. To find its circumference, you can follow these steps:

  1. The radius of the cookie is 3 inches.
  2. C = 2πr = 2π x 3 = 18.8 inches.
  3. Rounding to one decimal place, the circumference is 18.8 inches.

How to solve word problems involving circumference?

Sometimes, you may encounter word problems that require you to find the circumference of a circle or use the circumference to find other information. To solve these problems, you need to read the problem carefully, identify the given information and the unknown quantity, and use the appropriate formula for circumference. Here are some examples of word problems involving circumference:

Example 1

A circular pond has a diameter of 12 meters. What is the length of the fence that surrounds the pond?

Solution:

In this problem, we are given the diameter of the pond and we need to find the length of the fence. The length of the fence is equal to the circumference of the pond. We can use the formula C = πd to find the circumference.

  • The diameter of the pond is 12 meters.
  • C = πd = π x 12 = 37.7 meters (rounded to one decimal place).
  • The length of the fence is 37.7 meters.

Example 2

A bicycle wheel has a radius of 35 centimeters. How many times does the wheel turn when the bicycle travels 1 kilometer?

Solution:

In this problem, we are given the radius of the wheel and we need to find the number of times it turns. The number of times the wheel turns is equal to the distance traveled divided by the circumference of the wheel. We can use the formula C = 2πr to find the circumference.

  • The radius of the wheel is 35 centimeters.
  • C = 2πr = 2 x π x 35 = 219.9 centimeters (rounded to one decimal place).
  • The distance traveled is 1 kilometer, which is equal to 100,000 centimeters.
  • The number of times the wheel turns is 100,000 / 219.9 = 454.75 (rounded to two decimal places).

How to practice finding the circumference of a circle?

One of the best ways to practice finding the circumference of a circle is to use worksheets that provide different types of problems and challenges. Worksheets can help you review the formulas, apply them to various situations, and check your answers. You can find many worksheets online that are suitable for different grade levels and skill levels. Here are some examples of worksheets that you can use to practice finding the circumference of a circle:

Circumference of a circle worksheet

This worksheet contains six standard problems and two word problems that require you to find the circumference of a circle given its radius or diameter. You can choose between customary units (inches, feet, yards) or metric units (centimeters, meters). You can also choose whether to use the exact value of pi or an approximation. This worksheet is suitable for grade 5 and above.

You can download this worksheet from K5 Learning.

Radius or diameter from circumference worksheet

This worksheet contains eight problems that require you to find the radius or diameter of a circle given its circumference. You need to divide the circumference by pi or 3.14 to get the diameter, and then divide it by two to get the radius. This worksheet is suitable for grade 6 and above.

You can download this worksheet from Math Fun Worksheets.

Circumference from area worksheet

This worksheet contains eight problems that require you to find the circumference of a circle given its area. You need to use the formula A = πr^2 to find the radius, and then multiply it by 2π to get the circumference. This worksheet is suitable for grade 7 and above.

You can download this worksheet from Math Worksheets 4 Kids.

Conclusion

In this lesson, you have learned how to find the circumference of a circle using the diameter or the radius. You have also learned how to use the circumference to find other information, such as the diameter, the radius, or the number of times a wheel turns. You have practiced solving word problems involving circumference using different formulas and methods. You have also used worksheets to review and reinforce your skills. Finding the circumference of a circle is an important skill that you can use in many real-life situations, such as measuring distances, designing objects, or estimating areas. We hope you enjoyed this lesson and found it useful.


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