Mathematics
CIRCUMFERENCE AND AREA OF A CIRCE
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CIRCUMFERENCE AND AREA OF A CIRCE
In this chapter, students will learn how to calculate the circumference of a circle, solve word problems involving the circumference of a circle, calculate the area of a circle, and solve word problems involving the area of a circle.
Circumfere nce of a circle
The circumference of a circle is the total distance around the circle.
Identify the concept of circumference of a circle
Activity 1
Study from the following informationThe circumference of a circle is the total distance around the circle. It is similar to the perimeter of other shapes, but for a circle we use the special term circumference. In simple terms:Circumference = Distance around a circle For example, if a string is placed around a plate or a wheel, the length of that string represents the circumference. The circumference depends on the size of the circle. The larger the circle, the greater the circumference.
Calculate the circumference of different circles
Activity 2
Read careful the following information. The circumference of a circle is the distance around the circle. There are two main formulas, depending on the information given.
Example 1
Observe the following examples
Example 2
Study the following examples
Exercise 1
Answer the following questions
- A circular playground has a radius of 16m. The school wants to put a rope all the way around it. Calculate the length of rope needed.
- A bicycle wheel has a diameter of 70 cm. Find its circumference
- How far does the bicycle move after one full rotationof the wheel? b) If the wheel rotates 10 times, what total distance is covered?
- A circular plate has a diameter of 10 cm. Calculate the circumference.
- A circle has a radius of 3.5 cm. Calculate the circumference. (Use π = 22/7)
- A circular table has a circumference of 94.2 cm. Find the diameter of the table.
- A circular water tank has a diameter of 3 m.
- a) Calculate the distance around the tank. b) If a person walks around the tank 5 times, how far do they walk?
- A bicycle wheel has a diameter of 70 cm. How far does the bicycle move after one rotation?
- A circular running track has a radius of 2.8 m. Find the total distance around the track.
- A circle has a circumference of 6 cm. Find its radius.
- A bracelet forms a perfect circle with radius 3.5 cm. Determine the length of wire needed.
Solve word problems involving circumference of a circle
Example 3
Study the following examples
Example 4
Exercise 2
Solve the following problems
Area of a cirle
Identify the concept of a circle
The area of a circle refers to the amount of two-dimensional space enclosed within its boundary (the circumference). It tells us how much surface the circle covers on a flat plane.
Calculate area of circle
Activity 3
Observe the following information
Activity 4
Study from the following information
Exercise 3
Solve the following problems
Area of a circle is calculated as:
Example 5
Study the following examples
Exercise 4
Solve word problems involving circle
Activity 5
Study the following examples
Example 6
Study the following examples
Example 7
Example 8
A circular lid has a diameter of 20 cm. Find the area of the lid.
Example 9
7. A circular roundabout has a radius of 8 m. Find the area of the roundabout.
Example 10
A circular flower bed has a radius of 3.5 m. Find the area of the flower bed.
Example 11
A circular sports field has a diameter of 50 m. Calculate the area of the field.
Exercise 5
Solve the following problems
- 1. A circular mirror has a radius of 18 cm. a) Find the area of the mirror. b) If the mirror is to be decorated with a border, what is the area to cover?
- 2. A circular pool has a diameter of 10 m. a) Find the area of the pool surface. b) How much material is needed to cover the pool?
- 3. A flower garden has a radius of 4 m. a) Determine the area of the garden. b) If grass is planted, how much area will be covered by grass?
- 5. A circular water tank lid has a radius of 1.5 m. a) Find the area of the lid. b) How much paint is needed to paint the lid?
- 6. A circular carpet has a diameter of 3 m. a) Calculate the area of the carpet.b) If a designer wants to make a pattern covering the whole carpet, what is the area to cover?
- 7. A small circular clock has a radius of 8 cm. a) Find the area of the clock face. b) If a protective glass is placed, how much area does the glass cover?
- 8. A circular table has a radius of 1.2 m. a) Calculate the area of the table surface. b) How much tablecloth is needed to cover it completely?
- 9. A small circular patch in a playground has a diameter of 6 m. a) Find the area of the patch. b) If it is filled with sand, how much area will the sand cover?
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