Circles, Arcs & Sectors (CIE IGCSE Maths: Core)

A circle has a circumference of 56mm.

Work out the radius of this circle.

.............................mm 

Rachel has a pond in her garden in the shape of a circle.
The circumference of the pond is 4.25m.

Calculate the diameter of the pond.
Give your answer in centimetres.

............................................ cm

is a sector of a circle with radius 9 cm and centre .
The angle at is 30°.

Calculate the area of this sector.
Give your answer in terms of .

......................................... cm² 

The diagram shows a semicircle with diameter 9 cm.

Calculate the total perimeter of this semicircle.

......................................... cm 

There is a circular pool in the play area at a park.
The pool has a diameter of 8m.

Calculate

..........................m [2]

........................... m² [2]

The diagram shows a circle, centre , radius 11 cm.
and are points on the circumference of the circle.
The line touches the circle at and is parallel to the line .
is a point on and angle = 140°.

Write down the mathematical name of the straight line.

Find, in terms of , the circumference of the circle.

[2]

Work out angle .

Angle = ................................................. [2]

The diagram shows a square with vertices on the circumference of a circle, centre .
The radius of the circle is 6 cm.

Work out the shaded area.

.......................................... cm² 

Points and are on the circumference of a semicircle, centre and radius 8 cm.
Angle = 90°.

Calculate the shaded area.

.........................................cm² 

The diagram shows a rectangle and two semicircles with diameters  and .
This diagram is a scale drawing of a running track.

1 centimetre represents ............................ metres.

[2]

This shape is drawn using two semicircles that have the same centre.
The large semicircle has radius 7 cm.
The small semicircle has radius 3 cm.

Calculate the area of the shape.

.............................. cm²