Circles, Arcs & Sectors (Edexcel GCSE Maths: Foundation)

On the left circle below, draw a sector and shade it in. Label it "sector".

On the right circle below, draw a segment and shade it in. Label it "segment".

The diagram below shows a semicircle with diameter 50 m.

Find the perimeter of the semicircle.

Give your answer in an exact form.

A new sign for an ice cream shop has been designed.

It consists of a semicircle and an isosceles triangle.

The dimensions of the sign are shown in the diagram below.

Calculate the total area of the sign to 3 significant figures.

.................... cm²

The diagram below shows sector .

Given that the area of the sector  is  cm², find the value of .

The diagram below shows sector .

Given that the length of the arc  is  cm, find the value of .

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

i) the circumference of the pool,

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

ii) the area of the pool.

........................... m² [2]

Write down the mathematical terms associated with circles that can be described by the following definitions:

(i) A line passing through the centre of the circle, which intersects the circle in one place only.

(ii) An area formed by two radii.

(iii) An area formed by a chord.

The diagram below shows a semicircle and a circle.

The diameter of the semicircle is 16 cm.

The radius of the circle is cm.

Given that the area of the semicircle is 8 times larger than the area of the circle, find the value of .

The diagram shows a sector  of a circle, centre  and radius 6 cm.

is a right-angled triangle.

Work out the area of the shaded segment .

Give your answer to 3 significant figures.

...................... cm²

The shaded shape below, , is formed by taking a large sector, , and removing a smaller sector, .

Find the shaded area, stating your answer in terms of .

For the same shape described in part (a)

Find the perimeter of the shape , stating your answer in terms of .

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.

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

[2]

ii) Work out angle .

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

iii) Calculate the length of the minor arc .

............................................ cm [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 

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

i) Complete the statement.

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

[2]

ii) Work out the total length of the running track in metres.

............................. m [3]

iii) Shreva walks at 1.4m/s.

Work out how long it will take her to walk once around the track.
Give your answer in minutes and seconds, correct to the nearest second.

.................... minutes .................... seconds [3]

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