1. Solve Problems Involving the Circumference and Area of Circles
We are Learning to……
Solve Problems Involving the Circumference and Area of Circles

2. The circumference of a circle
For any circle,
π =
circumference
diameter
or,
π = C d
We can rearrange this to make a formula to find the circumference of a circle given its diameter.
Pupils should be asked to learn these formulae.
C = πd

3. Finding the circumference given the radius
The diameter of a circle is two times its radius, or
d = 2r
We can substitute this into the formula
C = πd
to give us a formula to find the circumference of a circle given its radius.
C = 2πr

4. Finding the radius given the circumference
Use π = 3.14 to find the radius of this circle.
C = 2πr
12 cm
How can we rearrange this to make r the subject of the formula? C 2π
r = ?
Link:
A3 Formulae – changing the subject of a formula 12
2 × 3.14 =
= 1.91 cm (to 2 d.p.)

5. Find the perimeter of this shape
Use π = 3.14 to find perimeter of this shape.
The perimeter of this shape is made up of the circumference of a circle of diameter 13 cm and two lines of length 6 cm.
13 cm
6 cm
Perimeter = 3.14 ×
= cm

6. Formula for the area of a circle
We can find the area of a circle using the formula
Area of a circle = π × r × r
radius or
Area of a circle = πr2

7. Finding the area given the diameter
The radius of a circle is half of its radius, or
r = d 2
We can substitute this into the formula
A = πr2
to give us a formula to find the area of a circle given its diameter.
A =
πd2 4

8. Find the area of this shape
Use π = 3.14 to find area of this shape.
The area of this shape is made up of the area of a circle of diameter 13 cm and the area of a rectangle of width 6 cm and length 13 cm.
Area of circle = 3.14 × 6.52
13 cm
6 cm
= cm2
Compare this with slide 74, which finds the perimeter of the same shape.
Area of rectangle = 6 × 13
= 78 cm2
Total area =
= cm2

9. Area of a sector What is the area of this sector? Area of the sector =
72°
360°
× π × 52
72°
5 cm 1 5
= × π × 52
= π × 5
Discuss how this area could be calculated before revealing the solution.
The area of a sector is a fraction of the area of a full circle. We can find this fraction by dividing the angle at the centre by 360°.
= 15.7 cm2 (to 1 d.p.)
We can use this method to find the area of any sector.

10. Circumference and Area of a Circle
The Circumference of a circle can be calculated using the formulae:
C = 2πr or C = πd
The Area of a circle can be worked out by using the formula:
A = πr²
Where d is the diameter, r is the radius and π = 3.14 to 2 decimal places
Circles 3 Word Problems #s 2, 4, 6, 7, 9, 11, 12 & 14

11. Extra Practice
Using the appropriate formula, work out the circumference and area for the following circles:
1. r = 4 cm Use π = 3.14
2. d = 7 cm The formulae are:
3. r = 6 cm C = 2πr
4. d = 9 cm C = πd
5. r = 7 cm A = πr²