3 10.1 Circumference and area of a circle
Questions are targeted at the grades indicated
Guided practice worksheet
1
Write down the names of the labelled parts of the circles below.
a
a
a
a
b
b
b
c
c
c
......................
d
d
d
......................
b
......................
c
d
......................
e
.....................
e
e
f
f
f
g
g
g
e
f
......................
g
......................
h
......................
h
h
h
2
D
For each of these circles work out:
i the circumference
ii the area.
a
i
.................
b
i
.................
c
i
6 cm
6 cm
6 cm
6 cm
mm
mm
mm
mm
1818
18
18
5 cm
5 cm
5 cm
5 cm
ii
3
ii .................
.................
.................
d
i
.................
7 mm
7 mm
7 mm
7 mm
ii .................
ii .................
C
Work out the perimeter and area of the following shapes.
a
b
c
d
8 mm
5 cm
2 cm
10 cm
8 cm
......................
4
......................
12 cm
......................
14 mm
......................
A gardener makes a circular rose bed of radius 1 m in the centre of a rectangular lawn, measuring 5 m by 4 m.
Calculate the area of the lawn after the rose bed has been made.
.........................................................................................................
5
A bicycle wheel has a circumference of 88 inches.
Calculate the radius of the wheel to the nearest inch.
.........................................................................................................
6
A circle and a square have the same area.
The square has sides of 6 cm.
Calculate the radius of the circle.
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281
3 10.2–10.3 Sectors; Problems involving circles in terms of π
Guided practice worksheet
1
Questions are targeted at the grades indicated
D
Calculate, in terms of π, the i circumference, ii area of the circles with radius or diameter given below.
diameter = 12 cm
(i) circumference = 2πr = 2 × π × 6 = 12π cm
(ii) area = πr2 = π × 62 = 36π cm2
a radius = 4 cm
i
circumference = .................................................................
ii area = .................................................................
b radius = 32 mm
i
circumference = .................................................................
ii
area = .................................................................
c diameter = 7 cm
i
circumference = .................................................................
ii area = .................................................................
d diameter = 9 mm
2
i
circumference = .................................................................
ii
area = .................................................................
A
Calculate the i arc length ii perimeter and iii area of each sector, correct to 3 significant figures.
x
70
(i) Arc length = ––––– × 2πr = ––––– × 2 × π × 8.4 = 10.26 cm (3 sf)
360
360
70°
8.4 cm
(ii) Perimeter = radius + radius + arc = 8.4 + 8.4 + 10.26 = 27.06 cm (3 sf)
x
70
(iii) Area of sector = –––– × πr2 = ––––– × π × 8.42 = 43.1 cm2 (3 sf)
360
360
130°
6 mm
6 mm
130°
..........................................................................
5 cm
12°
120 mm
12°
ai
1.2 cm
250°
1.2 cm
20°
250°
120 mm
bi
..........................................................................
ii
..........................................................................
ii
..........................................................................
iii
..........................................................................
iii
..........................................................................
283A
3 10.2–10.3 Sectors; Problems involving circles in terms of π
Guided practice worksheet
A
20°
130°
6 mm
5 cm
250°
1.2 cm
20°
130°
12°
250°
120 mm
5 cm
1.2 cm
120 mm
ci
3
di
..........................................................................
..........................................................................
ii
..........................................................................
ii
..........................................................................
iii
..........................................................................
iii
..........................................................................
The diagram shows a plastic air vent.
a Calculate the area of one of the sector-shaped holes.
..............................................................................................................
b Calculate the area of plastic.
..............................................................................................................
..............................................................................................................
9 cm
20°
..............................................................................................................
10 cm
4
An outdoor infrared detector senses movement up to a distance of 8 m and scans an area of 75 m2.
8m
A*
Hint Substitute the values you know into:
x
x × πr2 and solve the equation
Area of sector = ––––
360
75 m2
Calculate the angle x.
..............................................................................................................
..............................................................................................................
283B
3 10.2–10.3 Sectors; Problems involving circles in terms of π
Guided practice worksheet
5
A
Calculate, in terms of π, the i arc length ii perimeter and iii area of each sector.
ai
arc length = .................................................................
6 cm
ii perimeter = .................................................................
120°
iii area = .................................................................
10°
4 mm
45°
bi
arc length = .................................................................
6 cm
120°
ii perimeter = .................................................................
10°
iii area = .................................................................
4 mm
6 mm
45°
ci
12 m
arc length = .................................................................
ii perimeter = .................................................................
iii area = .................................................................6 cm
120°
10°
4 mm
12 m
6 mm
45°
di
arc length = .................................................................
6 cm
ii perimeter 120°
= .................................................................
iii area = ................................................................. 10°
4 mm
45°
12 m
6 mm
283C
1
3 10.4 Units of area
Guided practice worksheet
1
Questions are targeted at the grades indicated
C
Convert the areas by multiplying.
Convert 0.54 m2 to mm2
1 m = 1000 mm so 1 m2 = 1000 mm × 1000 mm = 1 000 000 mm2
So 0.54 m2 = 0.54 × 1 000 000 mm2 = 540 000 mm2
a 0.25 m2 to mm2
b 1.4 m2 to cm2
..................................................................
..................................................................
..................................................................
..................................................................
c 3.4 cm2 to mm2
2
d 0.024 m2 to cm2
..................................................................
..................................................................
..................................................................
..................................................................
Convert the areas by dividing.
Convert 3500 cm2 to m2
1 m = 100 cm so 1 m2 = 100 cm x 100 cm = 10 000 cm2 so divide by 10 000
So 3500 cm2 = 3500 ÷ 10 000 m2 = 0.35 m2
a 4500 cm2 to m2
b 34 000 cm2 to m2
..................................................................
..................................................................
..................................................................
..................................................................
c 320 mm2 to cm2
3
d 4000 mm2 to cm2
..................................................................
..................................................................
..................................................................
..................................................................
Convert the following areas by multiplying or dividing.
a 0.42 cm to mm
2
2
............................................................................................................
Multiply if converting to
a smaller unit, divide if
converting to a larger unit.
b 62 000 mm2 to m2 ............................................................................................................
c 237 mm2 to cm2 ............................................................................................................
d 5200 cm2 to m2 ............................................................................................................
e 0.0044 m2 to cm2 ............................................................................................................
f 0.24 cm2 to mm2 ............................................................................................................
g 350 mm2 to cm2 ............................................................................................................
h 420 000 mm2 to m2 ............................................................................................................
4
A roll of card has an area of 43 m2. A postcard has an area of 125 cm2. How many postcards can be cut
from the roll, assuming there is no wastage?
......................................................................................................................................................................................................................................
285A
3 10.4 Units of area
2 mm
2 mm
Guided practice worksheet
5
C
Calculate the area of each shape in i mm2 ii cm2
6.2 mm
2 mm
6.2 mm
1.4 m
2.35 m
1.4 m
7 mm
7 mm
2.35 m
6.2 mm
4.2 cm
1.4 m 63 cm
63 cm
4.2 cm
7 mm
2.35 m
4.2 cm
63 cm
6
a i mm2 = ........................................
b i mm2 = ........................................
c i mm2 = ........................................
ii cm2 = ........................................
ii cm2 = ........................................
ii cm2 = ........................................
The diameter of a 1p coin is 20.3 mm.
a Calculate its area, in mm2.
.................................................................................................................................................................................................................................
A sheet of metal measuring 33 cm by 2.6 m is used to make some coins.
b Calculate the area of the sheet, in cm2.
.................................................................................................................................................................................................................................
c Estimate the maximum number of coins that can be punched out of the sheet.
...........................................................................................................................................................................
Hint Find the number of
coins that would fit along
each edge of the sheet.
d Calculate the area of metal sheet remaining, in cm2.
.................................................................................................................................................................................................................................
7
Lauren paints a wall in rectangular strips measuring 2.3 m by 31 cm.
a Calculate the area of a rectangular strip, in cm2.
.................................................................................................................................................................................................................................
A tin of paint covers 30 m2 when applied using a roller.
b Calculate the number of strips that Lauren can paint from a single tin.
.................................................................................................................................................................................................................................
.................................................................................................................................................................................................................................
Lauren’s laser measure showed that a hall wall was 8323 mm by 2341 mm.
c How many rectangular strips would cover this area?
.................................................................................................................................................................................................................................
.................................................................................................................................................................................................................................
285B