MADE IN HULL
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BLADE
CIRCLES
POWERED BY
LOOK UP / BLADE
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SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)
WELCOME TO
MADE IN HULL
As part of the Made in Hull season (Jan-Mar),
Look Up features a series of temporary artistic
works created especially for Hull’s public
spaces and places.
As part of Look Up ‘Blade’ by Nayan Kulkarni,
in association with Siemens, will be installed
in Queen Victoria Square at the beginning
of January.
Blade is the inspiration for these Maths
resources. Designed for KS3 and KS4 students
they can form the basis of a number of
lessons or be used as part of a lesson about
angles, scale drawing or circles.
Use on a whiteboard, as a lesson plan or print
off worksheets for students to complete.
For more information about Look Up visit
.co.uk/lookup
hull
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Photo: © Octovision Media
Introduce Made in Hull by asking students if
anyone has seen Blade? What did they think?
SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)
Here’s Blade - what do you think?
Photo: © Tom Arran
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SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)
CIRCLES
Learning
Objectives
• Know parts of a circle
• Find the circumference and area of a circle
• Apply these to wind turbines
AREA AND CIRCUMFERENCE
OF CIRCLES
• A circle has radius (r)
and diameter (d)
• Circumference of a circle
C= d
• Area of a circle
A = r2
LOOK UP / BLADE
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SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)
CIRCLES
Learning
Objectives
• Know parts of a circle
• Find the circumference and area of a circle
• Apply these to wind turbines
Circumference
Ra
diu
s
AREA AND CIRCUMFERENCE
OF CIRCLES
• A circle has radius (r)
and diameter (d)
Sector
r
ete
m
Dia
• Circumference of a circle
C= d
Chord
Segment
• Area of a circle
Tan
ge
nt
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A = r2
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SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)
CIRCLES
PREPARE
Master
Calculate the area and circumference of
the circles with the following dimensions:
1) Radius of 4cm
4) Diameter of 5cm
A=
C=
A=
C=
2) Diameter of 3cm
5) Radius of 6cm
A=
C=
A=
C=
3) Diameter of 10cm
6) Diameter of 9cm
A=
C=
A=
C=
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r
d
Circumference of a circle
C= d
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Area of a circle
A = r2
SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)
CIRCLES
PREPARE
Answers
1) r = 4cm
2) d = 3cm
3) d = 10cm
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A = 50.27cm2
C = 25.13cm
A = 7.07cm2
C = 9.42cm
A = 79.54cm2
C = 31.42cm
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4) d = 5cm
5) r = 6cm
6) d = 9cm
A = 19.63cm2
C = 15.71cm
A = 113.10cm2
C = 37.70cm
A = 63.62cm2
C = 28.27cm
SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)
CIRCLES
Apply
PREPARE
Find the circumference and the ‘swept area’ of the nine wind turbines below.
What is the relationship between the power (given in KW) and the area and circumference
of the circle made?
250m
20,000kW
320
300
280
Past and present
Wind Turbines
260
Future Wind
Turbines
150m
10,000kW
240
Hub Height (m)
220
125m
5,000kW
200
180
100m
3,000kW
160
140
120
100
80
Rotor Diameter (m)
Rating (kW)
50m
750kW
60
40
17m
75kW
70m
1,500kW
80m
1,800kW
30m
300kW
20
0
1980- 1990-
1995-
2000-
2005-
1990
2000
2005
2010
1995
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2010-?
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2010-?
Future
Future
SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)
CIRCLES
Apply Extension
PREPARE
Given the ‘Swept area’ of this turbine, can you find the size
of the blades on each of them?
rea 133 sq
pt A
m
e
Sw
Turbine A
Gaia-Wind 133-11kW
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rea 45 s
pt A
q
e
m
Sw
Turbine B
SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)
LEARN MORE AT:
hull2017.co.uk/lookup
hull2017.co.uk/blade
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SEASON: MADE IN HULL l SUBJECT: MATHS (KS3 & KS4)