Transcript Document

GCSE
Mathematics
Targeting Grade C
SSM 3
Circles
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
a.
Know and use the vocabulary
associated with circles
b.
Know and use the value of pi (π)
c.
Remember the formula for the
circumference of a circle.
d.
Calculate the circumference of a
circle given the length of the
radius or the diameter
Remember the formula for
the area of a circle
e.
e.
Calculate the area of a circle
given either the length of the
radius or the diameter
f.
Solve problems involving the
circumference and area of a
circle
Questions
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
π
Find the value of
π in the following
three slides.
π =
(To 2 decimal places)
π =
(To 1 decimal places)
π =
(To 1 significant figure)
Circumference of a Circle
Circumference (C) Diameter (d) Radius (r)
C = π x d (C= πd)
C=2 x π x r (C=2 πr)
Circumference
Calculate the circumference of
the circles on the following slides
Example
A circular dish has a diameter of 9cm. Calculate the
circumference of the dish. (Take π = 3.14)
C=πxd
C = 3.14 x 9
9cm
C = 28.26cm
Example
A circle has a radius of 6cm. Calculate the circumference.
(Take π = 3)
Radius
= 6cm
Diameter = 12 cm (twice
the radius)
6 cm
C=πxd
C = 3 x 12
C = 36cm
Practice 1:
Find the
Circumference
5 cm
C=
(Take π = 3)
Practice 2:
Find the
Circumference
8 cm
C=
(Take π = 3)
Practice 3:
Find the
Circumference
12 cm
C=
(Take π = 3)
Practice 4:
Find the
Circumference
2 cm
C=
(Take π = 3)
Practice 5:
Find the
Circumference
6 cm
C=
(Take π = 3.1)
Practice 6:
Find the
Circumference
15 cm
C=
(Take π = 3.1)
Answers to all circumference practice questions
Practice answers - Circumference
1.
2.
3.
4.
5.
6.
C = π x d (π = 3, d = 5)
so C = 3 x 5 , C = 15cm.
C = π x d (π = 3, d = 8)
so C = 3 x 8, C = 24cm.
C = π x d (π = 3, d = 12)
so C = 3 x 12, C = 36cm
C = π x d (π = 3, r = 2, d is 4) so C = 3 x 4, C = 12cm
C = π x d (π = 3.1, d = 6)
so C = 3.1 x 6, C = 18.6 cm
C = π x d (π = 3.1, d = 15)
so C = 3.1 x 15, C = 46.5cm
Area of a circle
The formula for the area of a circle is
Area = π x radius x radius
A=πxrxr
A=πr²
Example 1 - Area
Work out the area of a circle with radius
5cm. (Take π = 3)
Area = π r²
A=πxrxr
5cm
A=3x5x5
A = 75cm²
Example 2 - Area
Work out the area of a circle with diameter 14cm.
Answer to 3 significant figures
(Take π = 3.14)
diameter = 16cm so
radius is 8cm
8cm
Area = π r²
A=πxrxr
A = 3.14 x 8 x 8
A = 200.96 cm²
A = 201cm² (to 3 s.f.)
Practice 1:
Find the Area
5 cm
A=
(Take π = 3)
Practice 2:
Find the Area
4 cm
A=
(Take π = 3)
Practice 3:
20 cm
Find the
Circumference and
Area
Answers to all area practice questions
C=
A=
(Take π = 3.14)
Practice answers - Area
1.
2.
3.
A = π r ² (π = 3, r = 5)
A=3x5x5
A = 75cm²
A = π r ² (π = 3, r = 4)
A=3x4x4
A = 48cm².
A = π r ² (π = 3.14, d = 20 so the radius is 10cm.)
A = 3 x 10 x 10
A = 300cm²
Questions
(i) The radius of a circle is 3.5 feet.
Calculate the circumference of
this circle.
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Answer
The radius is 3.5 so the
diameter is 7 feet
(i)
C=πxd
C = 3.14 x 7
C = 21.98 cm
(ii) Calculate the area of this circle.
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(4)
Take π = 3.14
(ii)
A=πr²
A=πxrxr
A = 3.14 x 3.5 x 3.5
A = 38.465cm²
A = 38.46cm² (2dp)
(a) Calculate the area of a circle
with radius 1.2 cm.
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(2)
(b) What is the radius of a circle
with an area of 66 cm²?
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(3)
Answer
The radius is 1.2 cm
(a)
A=πr²
A=πxrxr
A = 3.14 x 1.2 x 1.2
A = 4.5216cm²
A = 4.52cm² (2dp)
(b) A = π r ²
66 = π x r ²
Take π = 3.14
66 = 3.14 x r ²
r =  (66 ÷3.14)
r = 4.58cm (2dp)
a) A circle has a diameter of 7 cm.
(i) Calculate the circumference of this
circle.
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(ii) Calculate the area of this circle.
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Answer
The diameter is 7cm so the
radius is 3.5cm
(a)
(i)
C = 21.98 cm
(ii)
Take π = 3.14
A=πr²
A=πxrxr
(b) A plastic beaker has a height of 10
cm and a circular base of diameter
7 cm.
Calculate the volume of the beaker.
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C = 3.14 x 7
A = 3.14 x 3.5 x 3.5
A = 38.465cm²
A = 38.46cm² (2dp)
(b)
V = area of cross section x h
V = 38.465 x 10
V = 384.65 cm³