Circumference and Area of a Circle

2. PARTS OF A CIRCLE
Distance around the outside =
Circumference (C)
Centre
Diameter (D)
Radius (r)
Area (A)
The space inside the boundary of a circle =

3. RULES FOR CIRCUMFERENCE
OF A CIRCLE
Circumference (C)
Diameter (D)
Radius (r)
C = 𝝅D
C = 2𝝅r
Use the 𝝅 button
on your calculator
Circumference = 𝝅 x Diameter
Circumference = 2 x 𝝅 x radius

4. EXAMPLES
12 cm
7mm
Find the circumference of these circles (rounding your answer to 2 decimal places):
1. 2.
C = 𝝅D
C = 𝝅 x 12
C = 37.69911184
C = 37.70 cm
C = 2𝝅r
C = 2 x 𝝅 x 7
C = 43.98229715
C = 43.98 mm

5. PERIMETER OF A SEMI-CIRCLE
Perimeter = distance around the outside of a shape
The perimeter of a semi-circle is made up of a straight line and a curved line.
Straight line = diameter
Curved line = half of the circumference
Perimeter = half the circumference + diameter
P =
𝐂
𝟐
+ D

6. PERIMETER OF A QUARTER-CIRCLE
Perimeter = distance around the outside of a shape
The perimeter of a quarter-circle is made up of 2 straight lines and a curved line.
Straight line = radius
Curved line = quarter of the circumference
Perimeter = quarter of the circumference + 2 x radius
P =
𝐂
𝟒
+ 2r

7. EXAMPLES
1. 2.
P =
𝐂
𝟐
+ D
P =
𝜋D
2
+ D
P =
𝜋 x 9
2
+ 9
P = 23.14 m
P =
𝐂
𝟒
+ 2r
P =
2𝜋r
4
+ 2r
P =
2 x 𝜋 x 3
4
+ 2 x 3
P = 10.71 cm

8. RULE FOR AREA OF A CIRCLE
Area (A)
Diameter (D)
Radius (r)
A = 𝝅r2
Use the 𝝅 button
on your calculator
Area = 𝝅 x radius squared

9. EXAMPLES
12 cm
7mm
Find the area of these circles (rounding your answer to 2 decimal places):
1. 2.
A = 𝝅r2
A = 𝝅 x 72
A = 153.93804
A = 𝝅r2
A = 𝝅 x 62
A = 113.0973355
Area = 153.94 mm2
Radius = 6cm
Area = 113.10 cm2

10. AREA OF A SEMI-CIRCLE
Diameter
Radius = half of the diameter
Area = half the area of a full circle
A = ½ 𝝅r2 Or you can use
A = 𝝅r2 ÷ 2

11. AREA OF A QUARTER-CIRCLE
Straight line = radius
Area = quarter of the full area of a circle
A = ¼ 𝝅r2 Or you can use
A = 𝝅r2 ÷ 4

12. EXAMPLES
1. 2.
A = ½ 𝝅r2
A = ½ x 𝝅 x 4.52
A = 31.80862562
Area = 31.81 m2
A = ¼ 𝝅r2
A = ¼ x 𝝅 x 32
A = 7.06853471
Area = 7.07 cm2

13. THE END