Circle Calculations
1. Each diagram below shows a cut-off circle with a horizontal base.
OA is a radius of the circle. Calculate h.
(a)
(b)
O
h
O
15cm
A
(c)
h
O
40cm
22cm
A
h
7.5cm
60cm
A
12cm
2. In each circle below OP is a radius. Calculate x.
x
(a)
(b)
P
12cm
60cm
O
O
7cm
35cm
P
x
(c)
(d)
O
O
5.5m
18cm
8m
x
P
22cm
x
P
3. The diagrams below shows an arc of a circle with radius OA. Calculate h.
(a)
(b)
110cm
15cm
h
A
h
A
80cm
9.8cm
O
O
4. The diagram opposite shows the cross-section
of a tunnel. This cross-section is in the shape
of a circle with a horizontal floor.
The radius of the circle is 3 metres.
The floor of the tunnel, AB, is 4.8 metres.
h
O
3m
Calculate h, the height of the tunnel.
A
A
5. The diagram opposite shows a table.
The table is in the shape of a circle
with a straight edge.
The radius OA of the table is 50 cm
and AB is 72cm.
B
4.8m
72cm
B
50cm
O
w
Calculate w, the width of the table.
300m
6. The diagram shows the side view of a bridge
in the shape of an arc of a circle.
O is the centre of the circle which has radius
220 metres.
AB is 300 metres.
Calculate the distance h.
h
A
B
220m
O
7. The diagram opposite shows a cylindrical oil tank.
AB = 4 metres and the radius OA = 3 metres.
O
3m
Calculate the depth d metres.
4m
A
d
A
8. A logo for a company is in the shape of a circle
with a horizontal top.
The radius OA of the circle is 20 cm and the
distance AB is 30 cm.
30cm
B
B
20cm
O
h
Calculate h, the height of the logo.
9. The diagram opposite shows a water tank with
a circular cross-section.
The radius of the tank is 4.6 metres and the
width of the surface of the water in the tank
is 6.8 metres.
O
4.6m
Calculate d, the depth of water in the tank.
A
6.8m
d
w
A
10. The diagram opposite shows a circular piece
of wood with the top sawn off.
The circle has radius OA = 55 centimetres.
Calculate w, the width of the straight edge
of the wood.
55cm
O
80cm
B
Arcs and Perimeter
1. Each diagram shows an arc of a circle with a straight edge. O is the centre
of the circle.
Calculate the perimeter of each shape.
(a)
(b)
12cm
25cm
O
O
(c)
(d)
1400
6.6cm
O
O
1300
(e)
(f)
O
3.2m
1600
50 0 O
26cm
60mm
2. The diagram shows a table top in the shape
of part of a circle, centre O, radius 55 cm.
Calculate the perimeter of the table top.
75 0 O
55cm
3. A school badge is in the shape of a circle
with a straight edge, as shown.
O represents the centre of the circle which
has radius 4.5 cm.
Braid is sewn round the edge of the badge.
How long will the braid be?
O
SHS
4. A kitchen worktop is in the shape of part of
a circle with a straight edge so that it can be
fitted against a wall.
The radius of the worktop is 75 cm and O
represents the centre of the circle.
Calculate the perimeter of the worktop.
5. The diagram shows a garden, circular in shape,
with a straight edge. O represents the centre of
the circle which has radius 32 metres.
A wall is to be built around the outside of the
garden. How long will the wall be?
32 m
O