Circles 1.
The Circumference.
Circumference = π x diameter
Circumference = 2 x π x radius
C = πd
C = 2πr
1).
Use π = 3.14. Calculate the circumference of each circle to 2 d.p., if the diameter is :
a). 12 cm
b). 20 cm
c). 35 cm
d). 90 cm
e). 2 cm
f). 6.5 cm
g). 10.5 mm h). 0.5 Km
i). 105.1 m j).
6.35 m
k). 88.15 mm l). 80.05 cm m). 25.6 Km n). 23.34 Km o). 323 mm
p). 4502 cm q). 0.125 Km r). 1.625 m s). 11.65 cm t).
3045 m
2).
Measure the diameter of each of these circles and calculate their circumferences to 1 d.p..
Take π = 3.142.
a).
d).
c).
b).
e).
h).
g).
f).
i).
a).
j).
3).
Using the π button on your calculator, calculate the circumference of these circles to 2 d.p.
when the radius is:
a). 10 cm
b). 55 cm
c). 12 m
d). 560 m
e). 490 Km
f). 0.6 mm
g). 0.125 m h). 35.8 mm i). 345 Km j).
80.04 Km
k). 0.04 m
l). 0.012 Km m). 23.99 cm n). 1000 Km o). 987.6 m
p). 64 ft
q). 20.25 yds r). 4.75 miles s). 50 in
t).
6.5 ft.
4).
Measure the radii of each of these circles and calculate their circumferences to 3 d.p..
Take π = 3.142.
c).
e).
b).
d).
Level 6 Pack 5. Page 33.
Licensed to Surbiton High School
[email protected]
h).
f).
g).
k).
i).
j).
For the following questions use calulator π and leave answers to a sensible degree of accuracy.
5).
The minute hand on a watch is 1.5 cm long. What distance does the tip of this hand travel
through in
a). 1 hour ?
b). 1 day ?
6).
A farmer has a circular field which is 250 metres across. He wishes to put a fence around
the field. What length of fencing does he require ?
7).
A bicycle tyre has a 40 cm radius.
a). If the wheel travels through 1 complete revolution, how far has the bicycle travelled?
b). The wheel rotates 120 times, how far has the bicycle travelled ?
8).
A car tyre has a 55 cm radius.
a). If the wheel travels through 1 complete revolution, how far has the car travelled?
b). The wheel rotates 2500 times, how far has the car travelled
i).
in cm,
ii). in m,
iii). in Km ?
9).
The following shapes are made up of full circles, semi-circles or quarter circles.
Find the circumference of each of the following shapes.
b).
c).
a).
7m
12 cm
d).
22 m
7m
22 m
e).
8 cm
f).
43 cm
15 m
8 cm
15 m
43 cm
g).
h).
i).
50 m
17 mm
30 m
30 m
12 mm
17 mm
12 mm
50 m
Level 6 Pack 5. Page 34.
Licensed to Surbiton High School
[email protected]
Circles 2.
The Area.
Area = π x radius x radius
1).
2).
A = πr2
Use π = 3.14. Calculate the area of the circle to 2 d.p., if the radius is :
a). 10 cm
b). 25 cm
c). 66 cm
d). 72 cm
e).
f). 9 Km
g). 6.5 mm
h). 90.2 Km i).
45 m
j).
k). 30.55 mm l). 2.01 cm
m). 2.5 Km
n). 405 Km o).
p). 23 cm
q). 4.5 Km
r). 3.25 m
s). 0.75 cm t).
0.5 cm
550 m
80 mm
4.25 m
Measure the radii of each of these circles and calculate their areas to 1 d.p.. Take π = 3.14.
a).
b).
c).
d).
j).
e).
g).
h).
j).
f).
i).
3).
Calculate the area of the circle to 2 d.p., using the π button, if the diameter is :
a). 30 mm
b). 26 cm
c). 88 m
d). 120 cm
e). 256 Km
f). 2500 Km g). 84.6 mm h). 0.2 Km
i).
48.4 m
j). 32.5 m
k). 0.1 mm
l). 6 cm
m). 220 Km n). 50 Km
o). 43 mm
p). 8 ft
q). 5.5 miles r). 22.25 ft
s). 7.5 yds
t). 2000 inches.
4).
Measure the diameters of each of these circles and calculate their areas to 1 d.p..
Take π = 3.142.
c).
b).
e).
a).
d).
Level 6 Pack 5. Page 35.
Licensed to Surbiton High School
[email protected]
f).
g).
i).
j).
h).
5).
a).
e).
i).
m).
q).
Find the area of the following circles. Take π = 3.14. Leave the answer to 3 sig. figs..
radius = 7 cm
b). radius = 28 m
c). radius = 1.4 Km d). radius = 5.6 m
diam. = 28 m
f). diam. =112 mm g). diam. = 84 cm h). diam. = 3.5 m
radius = 490 m j). radius = 0.49cm k). diam. = 7 mm l). diam. 24.5 Km
radius = 1.75 cm n). diam. = 168 Km o). radius = 1.33 m p). diam. = 119 yds
radius = 0.28 m r). radius = 3500 ft s). diam. = 0.47 m t). radius = 630 miles.
For the following questions use calulator π and leave answers to a sensible degree of accuracy.
6).
The minute hand on a watch is 2.5 cm long. Over what area does this hand travel in1 hour ?
7).
A farmer has a circular field which is 170 metres across. He wishes to cover it with plastic
sheeting. What area of sheeting does he require ?
8).
A circular table is 1.8 metres across. What is the area of the table top ?
9).
Rover is tied to a post in the middle of the garden with a rope 12 ft long.
On what area of the garden can poor little Rover walk ?
10). By measuring, what is the area in cm2 of one side of a
a). £1 coin
b). 10p coin c). 5p coin
d).
2p coin
e).
1p coin ?
11). The following shapes are made up of full circles, semi-circles or quarter circles.
Find the area of each of the following shapes.
a).
b).
c).
15 m
7m
d).
24 cm
e).
9 cm
15 m
f).
7m
21 mm
9m
9 cm
9m
21 mm
g).
h).
i).
60 m
46 mm
46 mm
25 m
25 m
32 mm
32 mm
60 m
Level 6 Pack 5. Page 36.
Licensed to Surbiton High School
[email protected]
Circles 3.
Leave answers to an appropriate degree of accuracy.
A).
B).
Take π = 3.14 in these questions.
Find the radii of these circles, if the circumference is:1). 31.4 cm 2). 18.84 m 3). 75.36 Km 4).
6). 232.36 mm 7). 113.04 m 8). 12.56 cm 9).
11). 40.192 Km 12). 45.844 cm 13). 88.548 m 14).
For the next set of questions use the calculator π.
16). 74 m
17). 15 cm
18). 124 mm 19).
21). 65 cm
22). 0.5 m
23). 34.2 mm 24).
26). 17.3 m
27). 146 mm 28). 95.3 cm 29).
Take π = 3.14 in these questions.
Find the radii of these circles, if the area is:1). 314 cm2 2). 78.5 m2 3). 706.5 Km2 4).
6). 50.24 mm2 7). 379.94 m2 8). 153.86 m2 9).
11). 78.4 Km2 12). 97.2 cm2 13). 68.9 m2
14).
For the next set of questions use the calculator π.
16). 94 m2
17). 55 cm2
18). 167 mm2 19).
2
2
21). 62.5 cm 22). 0.3 m
23). 54.2 mm2 24).
26). 23.3 m2
27). 106 mm2 28). 98.3 cm2 29).
314 mm 5). 87.92 cm
791.28 Km 10). 558.92 mm
172.072 m 15). 101.736 Km
65 Km
20). 46 m
2.7 m
25). 9.6 Km
1072 mm 30). 72 cm
1256 mm2 5). 200.96 cm2
306.25 m2 10). 547.1136 mm2
23 m2
15). 277.4504 Km2
68 Km2
20). 34 m2
2
6.7 m
25). 12.6 Km2
2072 mm2 30). 42 cm2
Worded Questions
Use the calculator π in all these questions.
1).
Susan makes a trundle wheel. The radius of the wheel is 0.2 metres. She pushes the wheel
across the playground. The wheel makes 30 complete revolutions.
Find the distance across the playground.
2).
Paul goes for a short cycle ride. Each wheel on his bike has a radius of 27 cm. His distance
counter tells him the wheel has rotated 650 times. Find how far he has travelled in metres.
3).
a).
b).
4).
The square and the circle have the same area.
a). Find the radius of the circle.
b). What is the circumference of the circle ?
Calculate the area of a circle with radius 1.6 cm.
What is the radius of a circle with an area of 60 cm2.
12 cm
12 cm
5).
Jenny goes for a long cycle ride. Each wheel on her bike has a radius of 18 cm.
Her distance counter tells her the wheel has rotated 5000 times.
Find how far she has travelled in Kilometres.
6).
The diagram shows a running track. BA and DE are
parallel and straight. They are 100 m long. BCD and
EFA are semicircular. They each have a diameter of
C
length 64 m.
a). Calculate the perimeter of the track.
b). Calculate the total area enclosed inside the track.
B
Level 6 Pack 5. Page 37.
Licensed to Surbiton High School
64 m
D
100 m
A
F
64 m
100 m
E
[email protected]
7).
a).
b).
A circle has a radius of 34 cm. Calculate its circumference.
The diagram shows four touching circles. Each circle has
a radius of 34 cm. P, Q, R and S are centres of the circles
and PQRS is a square.
i). What is the perimeter of the shaded region ?
ii). Calculate the area of the shaded region.
P
Q
S
R
E
8).
a).
b).
9).
Lynne goes for a cycle ride. Each wheel on her bike has a radius of 22 cm.
a). Find the circumference of her wheels.
b). Her distance counter tells her she has travelled 430 metres. How many times have
the wheels fully rotated ?
10). a).
b).
Calculate the area of a circle with a radius of 25 cm.
What is the radius of a circle with an area of 450 cm2 ?
Calculate the area of a circle with a radius of 2.8 m.
Many years ago the following rule was used to calculate the area of a circle.
Find 8 of the diameter. Square the result.
9
Use this rule to calculate the area of a circle with a radius of 1.3 m.
15 cm
11). This is the wire frame of a lampshade. It is made up of two circles of
wire and three straight lengths of wire.
a). The larger circle has a diameter of 30 cm. What is the circumference?
b). The straights are 20 cm each. The diameter of the smaller circle is 15 cm.
Calculate the total length of wire needed to make the frame.
20 cm
30 cm
12). Metal discs that have a radius of 12 cm can be remoulded into square metal sheets of the
same thickness.
a). I have 20 of the discs, what is the total area of metal that I have ?
b). This is to be made in to a square metal sheet. What size would this be ?
13). Billy does a sponsored bike ride. Each wheel on his bike has a radius of 30 cm.
a). Find the circumference of his wheels.
b). His distance counter tells him he has travelled 50 Kilometres.
How many times have the wheels completely rotated ?
14). Find the area and perimeter of the shaded regions in the following shapes.
a).
b).
c).
1.2 m
70 cm
0.9 m
d).
40 cm
30 cm
40 cm
e).
f).
10 cm
7m
7m
Level 6 Pack 5. Page 38.
12 cm
Licensed to Surbiton High School
5 cm
12 cm
[email protected]