Targeting Grade C

1
GCSE Mathematics
Targeting Grade C
SSM 3 Circles
2

• Know and use the vocabulary associated with
  circles
• Know and use the value of pi (p)
• Remember the formula for the circumference of a
  circle.
• Calculate the circumference of a circle given the
  length of the radius or the diameter
• Remember the formula for
• the area of a circle
• Calculate the area of a circle given either the
  length of the radius or the diameter
• Solve problems involving the circumference and
  area of a circle
• Questions

• Can you
• Calculate the circumference of a circle
• Calculate the area of a circle
• Solve (word) problems involving the circumference
  and/or area of a circle.
• Try these questions

If not you need to
3
Vocabulary and Definitions

• Circumference (Perimeter) the distance all the
  way round the edge of the circle.
• Diameter the distance from edge to edge passing
  through the centre of the circle
• Radius the distance from the centre of the
  circle to the edge

4
p

• Find the value of p in the following three
  slides. (slides 6, 7 and 8)

5
(To 2 decimal places)
p
6
(To 1 decimal places)
p
7
(To 1 significant figure)
p
8
Circumference of a Circle

• Circumference (C) Diameter (d) Radius (r)
• C p x d (C pd)
• C2 x p x r (C2 pr)

9
Circumference

• Calculate the circumference of
• the circles on the following slides
• (12 17)

10
Example

• A circular dish has a diameter of 9cm. Calculate
  the
• circumference of the dish. (Take p 3.14)

C p x d C 3.14 x 9 C 28.26cm
9cm
11
Example

• A circle has a radius of 6cm. Calculate the
  circumference.
• (Take p 3)

Radius 6cm Diameter 12 cm (twice the
radius) C p x d C 3 x 12 C 36cm
12
Practice 1 Find the Circumference
5 cm
C (Take p 3)
13
Practice 2 Find the Circumference
8 cm
C (Take p 3)
14
Practice 3 Find the Circumference
12 cm
C (Take p 3)
15
Practice 4 Find the Circumference
C (Take p 3)
16
Practice 5 Find the Circumference
6 cm
C (Take p 3.1)
17
Practice 6 Find the Circumference
15 cm
C (Take p 3.1)
Answers to all circumference practice questions
18
Practice answers - Circumference

• C p x d (p 3, d 5) so C 3 x 5 ,
  C 15cm.
• C p x d (p 3, d 8) so C 3 x 8,
  C 24cm.
• C p x d (p 3, d 12) so C 3 x 12,
  C 36cm
• C p x d (p 3, r 2, d is 4) so C 3 x 4,
  C 12cm
• C p x d (p 3.1, d 6) so C 3.1 x
  6, C 18.6 cm
• C p x d (p 3.1, d 15) so C 3.1 x
  15, C 46.5cm

19
Area of a circle

• The formula for the area of a circle is
• Area p x radius x radius
• A p x r x r
• A p r ²

20
Example 1 - Area

• Work out the area of a circle with radius
• 5cm. (Take p 3)

Area p r² A p x r x r A 3 x 5 x 5 A 75cm²
5cm
21
Example 2 - Area

• Work out the area of a circle with diameter 14cm.
  
• Answer to 3 significant figures
• (Take p 3.14)

diameter 16cm so radius is 8cm Area p r² A
p x r x r A 3.14 x 8 x 8 A 200.96 cm² A
201cm² (to 3 s.f.)
8cm
22
Practice 1 Find the Area
5 cm
A (Take p 3)
23
Practice 2 Find the Area
4 cm
A (Take p 3)
24
Practice 3 Find the Circumference and Area
20 cm
C A (Take p 3.14)
Answers to all area practice questions
25
Practice answers - Area

• A p r ² (p 3, r 5)
• A 3 x 5 x 5
• A 75cm²
• A p r ² (p 3, r 4)
• A 3 x 4 x 4
• A 48cm².
• A p r ² (p 3.14, d 20 so the radius is
  10cm.)
• A 3 x 10 x 10
• A 300cm²

26
Questions
27

• (i) The radius of a circle is 3.5 feet. Calculate
  the circumference of this circle.
• .............................................
• .............................................
• .............................................
• .............................................
• (ii) Calculate the area of this circle.
• .................................................
• .................................................
• ................................................
• .................................................
• (4)
• Take p 3.14

Answer

• The radius is 3.5 so the
• diameter is 7 feet
• C p x d
• C 3.14 x 7
• C 21.98 cm
• A p r ²
• A p x r x r
• A 3.14 x 3.5 x 3.5
• A 38.465cm²
• A 38.46cm² (2dp)

28

• Calculate the area of a circle with radius 1.2
  cm.
• ...............................................
• ...............................................
• ...............................................
• (2)
• (b) What is the radius of a circle with an area
  of 66 cm²?
• ...............................................
• ...............................................
• ...............................................
• (3)
• Take p 3.14

Answer

• The radius is 1.2 cm
• (a) A p r ²
• A p x r x r
• A 3.14 x 1.2 x 1.2
• A 4.5216cm²
• A 4.52cm² (2dp)
• A p r ²
• 66 p x r ²
• 66 3.14 x r ²
• r ? (66 3.14)
• r 4.58cm (2dp)

29

• a) A circle has a diameter of 7 cm.
• (i) Calculate the circumference of this circle.
• ..................................................
  .....
• ..................................................
  ....
• ..................................................
  .....
• .
• (ii) Calculate the area of this circle.
• ..................................................
  ......
• ..................................................
  .....
• (b) A plastic beaker has a height of 10 cm and a
  circular base of diameter 7 cm.Calculate the
  volume of the beaker.
• ..................................................
  ....
• ..................................................
  .....
• ..................................................
  .....
• ..................................................
  .....

Answer

• The diameter is 7cm so the
• radius is 3.5cm
• (a)
• (i) C 3.14 x 7
• C 21.98 cm
• A p r ²
• A p x r x r
• A 3.14 x 3.5 x 3.5
• A 38.465cm²
• A 38.46cm² (2dp)
• V area of cross section x h
• V 38.465 x 10
• V 384.65 cm³