targeting grade c
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GCSE Mathematics. Targeting Grade C. SSM 3 Circles. Know and use the vocabulary associated with circles Know and use the value of pi ( π ) Remember the formula for the circumference of a circle. Calculate the circumference of a circle given the length of the radius or the diameter - PowerPoint PPT PresentationTRANSCRIPT
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Targeting Grade CSSM 3Circles
GCSE Mathematics
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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
e. Remember the formula for the area of a circlee. 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
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
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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
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πFind the value of π in the
following three slides.
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(To 2 decimal places)
π =
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(To 1 decimal places)
π =
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(To 1 significant figure)
π =
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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)
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Circumference
Calculate the circumference of
the circles on the following slides
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ExampleA circular dish has a diameter of 9cm. Calculate
thecircumference of the dish. (Take π = 3.14)
9cm
C = π x dC = 3.14 x 9C = 28.26cm
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ExampleA circle has a radius of 6cm. Calculate the circumference. (Take π = 3)
6 cm
Radius = 6cmDiameter = 12 cm (twice the radius)
C = π x dC = 3 x 12C = 36cm
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5 cm
Practice 1:Find the
Circumference
C = (Take π = 3)
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8 cm
C = (Take π = 3)
Practice 2:Find the
Circumference
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12 cm
C = (Take π = 3)
Practice 3:Find the
Circumference
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2 cm
C = (Take π = 3)
Practice 4:Find the
Circumference
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6 cm
C = (Take π = 3.1)
Practice 5:Find the
Circumference
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15 cm C =
(Take π = 3.1)
Practice 6:Find the
Circumference
Answers to all circumference practice questions
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Practice answers - Circumference
1. C = π x d (π = 3, d = 5) so C = 3 x 5 , C = 15cm.
2. C = π x d (π = 3, d = 8) so C = 3 x 8, C = 24cm.
3. C = π x d (π = 3, d = 12) so C = 3 x 12, C = 36cm
4. C = π x d (π = 3, r = 2, d is 4) so C = 3 x 4, C = 12cm
5. C = π x d (π = 3.1, d = 6) so C = 3.1 x 6, C = 18.6 cm
6. C = π x d (π = 3.1, d = 15) so C = 3.1 x 15, C = 46.5cm
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Area of a circleThe formula for the area of a circle is
Area = π x radius x radiusA = π x r x rA = π r ²
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Example 1 - AreaWork out the area of a circle with
radius 5cm. (Take π = 3)
5cm
Area = π r²A = π x r x rA = 3 x 5 x 5 A = 75cm²
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Example 2 - AreaWork out the area of a circle with diameter
14cm. Answer to 3 significant figures (Take π = 3.14)
8cm
diameter = 16cm so radius is 8cm Area = π r²A = π x r x rA = 3.14 x 8 x 8A = 200.96 cm²A = 201cm² (to 3 s.f.)
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5 cm
A = (Take π = 3)
Practice 1:Find the Area
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4 cm
A = (Take π = 3)
Practice 2:Find the Area
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20 cm C =
A = (Take π = 3.14)
Practice 3:Find the
Circumference and Area
Answers to all area practice questions
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Practice answers - Area
1. A = π r ² (π = 3, r = 5) A = 3 x 5 x 5 A = 75cm²2. A = π r ² (π = 3, r = 4) A = 3 x 4 x 4 A = 48cm².3. A = π r ² (π = 3.14, d = 20 so the radius is
10cm.) A = 3 x 10 x 10 A = 300cm²
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Questions
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(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 π = 3.14
Answer
The radius is 3.5 so the
diameter is 7 feet(i) C = π x d C = 3.14 x 7 C = 21.98 cm
(ii) A = π r ² A = π x r x r A = 3.14 x 3.5 x
3.5 A = 38.465cm² A = 38.46cm²
(2dp)
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(a)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 π = 3.14
Answer
The radius is 1.2 cm(a) A = π r ²
A = π x r x r 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 66 = 3.14 x r ² r = (66 ÷3.14) r = 4.58cm (2dp)
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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.
......................................................
.......................................................
.......................................................
.......................................................
Take π = 3.14
Answer
The diameter is 7cm so the
radius is 3.5cm(a) (i) C = 3.14 x 7 C = 21.98 cm (ii) A = π r ²
A = π x r x r 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