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Circumference & Area of Circles

Exercise 1 – Circumference of Circles b. Radius

7. [Edexcel GCSE March2013-2H Q5]
1. Find the circumference of the following circles,
giving your answer to 1 decimal place.
a) b)

c) d) Jon has a flower garden in the shape of a circle.

The diameter of the garden is 5 metres.

Jon wants to put fencing around the edge of the

garden. The fencing costs £1.80 per metre.

Work out the total cost of the fencing. (3 marks)

2. Find the circumference, giving your answers in
exact form. 8. [Edexcel IGCSE Jan2017-1F Q17, Jan2017-3H Q4]
a) b)

3. A car wheel of diameter 35cm spins

on a road. The car moves forward
2000cm.
(a) What is the circumference of the
wheel?
(b) How many full rotations will the wheel have The diagram shows a design made from wire.
made?
The design is made from a square with side 70 cm,
4. A circular lawn has radius 10m. I encircle the lawn
a circle with diameter 40 cm, 4 straight pieces each of
with a hedge, which costs £35 per metre. What is
length 15 cm. Find the total length of wire needed for
the total cost, to the nearest pound?
the design. Give your answer correct to the nearest
5. The radius of the Earth is 6371km.
centimetre. (4 marks)
Light can travel 300,000km each
second. How many times can light 9. [Edexcel GCSE June2007-
encircle the Earth in a second? 4I Q13b] The diameter of
a wheel on Harry’s bicycle
is 0.65 m. Harry cycles
1000 metres. Calculate
6. The circumference of a circle is 100cm. the number of turns the
What is its: wheel makes. (2 marks)
a. Diameter
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10. [Edexcel GCSE Nov2014-2F Q26, Nov2014-2H the cost to seed the whole lawn?
Q11] Saphia is organising a conference. People at
the conference will sit at circular tables. 4. [Edexcel GCSE Nov2008-2F Q27, 4H Q6]
A circle has a radius of 6 cm. A square has a side
of length 12 cm. Work out the difference between
the area of the circle and the area of the square.
Give your answer correct to one decimal place.

5. The area of a circular disc is 100cm2. What is its

Each table has a diameter of 140 cm. diameter?
Each person needs around 60 cm around the
circumference of the table. 6. As the radius r of a circle increases, which graph
There are 12 of these tables in the conference room. shows how the area increases?
A total of 90 people will be at the conference. Are
there enough tables in the conference room?

 As the radius r of a circle increases, which graph

shows how the circumference increases?
Exercise 3 – Fractions of Circles
1. Find the area and perimeter of the following,
giving your answers to 1dp.
(a) (b)
Exercise 2 – Area of Circles
1. Find the area of the following circles, giving your
answer to 1 decimal place.
a) b)
(c) (d)

c) d)
2. Find the area and perimeter, giving exact
answers.
(a) (b)

2. Find the area of each circle, giving your answers in

exact form.
a) b)

3. Find the area and perimeter, giving exact

answers.

3. A circular lawn has radius 50m. Each box of grass

seed costs £5.99 and covers 60m2 of lawn. What is
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(a) (b) garden. Work out the cost of buying enough

fertiliser to cover the garden completely.

3. [Edexcel GCSE Nov2012-

1H Q12] The diagram
4. Fred Flintstone’s car has two different wheels: shows a circle drawn
one circular in shape and the other semi-circular. inside a square.
The diameter of the semi-circular wheel is 1.3m.
What radius is needed for the circular wheel so The circle has a radius of
that the wheels make the same number of full 6 cm. The square has a
circulations over any journey? (Give your answer side of length 12 cm.
to 3 decimal places) Work out the shaded area. Give your answer in
terms of π .

4. [OCR GCSE June 2016 2F Q19] This

diagram shows a circle inside a square.
The radius of the circle is 7 cm.
The length of a side of the square is 14
cm. Calculate the shaded area.

5. [Edexcel IGCSE May2014(R)-4H Q5] The diagram

Exercise 4 – Compound Shapes shows a metal plate in the shape of a rectangle.
Involving Circles The rectangle has length 20 cm and width 12 cm.
Two identical circles,
1. [Edexcel IGCSE each of diameter 6
June2011-3H Q15a] cm, have been cut
Here is a shape made out of the plate.
from a rectangle and a Work out the area
semicircle. The length of the shaded region
of the rectangle is 7.1 of the metal plate.
cm. The radius of the semicircle is 2.7 cm.
Give your answer correct to the nearest cm2.

Work out the area of the shape. Give your answer

6. [Edexcel Linked Pair June
correct to 3 significant figures.
2017 Methods 2F Q22,
Methods 2H Q10] A , B
2. [Edexcel GCSE(9-1)
and C are points on a
Mock Set 1 Autumn
circle with AC as a
2016 3F Q24a, 3H
diameter. ABC is a right-
Q7a] A garden is in the
angled triangle.
shape of a rectangle,
Work out the total area of
ABCD , and a
the regions shaded in the diagram. Give your
semicircle. AD is the
answer correct to 1 decimal place.
diameter of the
7. [Edexcel GCSE
semicircle.
Nov2016-2F Q28,
Nov2016-2H Q11] The
Carol is going to cover the garden with fertiliser. A
diagram shows a
box of fertiliser costs £4.99. Carol has been told
square ABCD inside a
that one box of fertiliser will cover 12 m 2 of
circle.
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The points A, B, C and D lie on the circle. logo that is shaded to show that Daisy is incorrect.
The radius of the circle is 6 cm. Work out the total
area of the shaded regions. Give your answer
correct to 3 significant figures. 12. [OCR GCSE(9-1) SAM 5H Q12] Three identical
small circles are drawn
8. [Edexcel GCSE(9-1) June 2017 3H Q8] A square, inside one large circle, as
with sides of length x cm, is inside a circle. shown in the diagram. The
Each vertex of the square is on the circumference centres of the small circles
of the circle. The area of the circle is 49 cm2. lie on the diameter of the
Work out the value of x . Give your answer correct large circle. Find the
to 3 significant figures. fraction of the large circle
that is shaded.
9. [Edexcel IGCSE May2016(R)-4H
Q7] Here are two circles. The  [Hamilton 2017 Q1] The diagram shows four
circles have the same centre O. equal arcs placed on the sides of a square. Each
The radius of the inner circle is 3 arc is a major arc of a circle
cm. The width of the shaded with radius 1 cm, and each
region between the inner circle side of the square has length
and outer circle is 2 cm. √ 2 cm. What is the area of
Work out the area of the shaded region. the shaded region?
Give your answer correct to 3 significant figures. Leave your answer in terms of
π.
10. [OCR GCSE(9-1) Nov 2018
2F Q21] A circle, with  [JMO 2008 A10] The perimeter of the shape
centre O and radius 6 cm, shown on the right is made from 20 quarter-
contains another circle, circles, each with radius 2 cm. What is the area of
with centre O and radius x the shape? Give your answer as an exact value.
cm. Write down an
expression, in terms of π  [UKMT] The diagram shows nine 1cm × 1cm
and x , for the shaded area squares and a circle. The circle passes through the
in cm2. centres of the four corner squares. What is the
11. [Edexcel GCSE(9-1) Nov 2017 area of the shaded region – inside two squares
1F Q26, Nov 2017 1H Q4 but outside the circle?
Edited] The diagram shows a
logo made from three circles.

Each circle has centre O .

1
Daisy says that exactly of
3
the logo is shaded. Find the actual fraction of the