Targeting Grade CSSM 3

Circles

GCSE Mathematics

a. Know and use the vocabulary associated with circles

b. Know and use the value of pi (π)

c. Remember the formula for the circumference of a circle.

d. Calculate the circumference of a circle given the length of the radius or the diameter

e. Remember the formula for the area of a circle

e. Calculate the area of a circle given either the length of the radius or the diameter

f. Solve problems involving the circumference and area of a circle

Questions

Can you:

•Calculate the circumference of a circle

•Calculate the area of a circle

•Solve (word) problems involving the circumference and/or area of a circle.

Try these questions

If not you need to

Vocabulary and Definitions

• Circumference (Perimeter) – the distance all the way round the edge of the circle.

• Diameter – the distance from edge to edge passing through the centre of the circle

• Radius – the distance from the centre of the circle to the edge

πFind the value of π in the

following three slides.

(To 2 decimal places)

π =

(To 1 decimal places)

π =

(To 1 significant figure)

π =

Circumference of a Circle

Circumference (C) Diameter (d) Radius (r)

C = π x d (C= πd)

C=2 x π x r (C=2 πr)

Circumference

Calculate the circumference of

the circles on the following slides

ExampleA circular dish has a diameter of 9cm. Calculate

thecircumference of the dish. (Take π = 3.14)

9cm

C = π x d

C = 3.14 x 9

C = 28.26cm

ExampleA circle has a radius of 6cm. Calculate the circumference. (Take π = 3)

6 cm

Radius = 6cm

Diameter = 12 cm (twice the radius)

C = π x d

C = 3 x 12

C = 36cm

5 cm

Practice 1:

Find the Circumference

C = (Take π =

3)

8 cm

C = (Take π =

3)

Practice 2:

Find the Circumference

12 cm

C = (Take π =

3)

Practice 3:

Find the Circumference

2 cm

C = (Take π =

3)

Practice 4:

Find the Circumference

6 cm

C = (Take π =

3.1)

Practice 5:

Find the Circumference

15 cm

C = (Take π =

3.1)

Practice 6:

Find the Circumference

Answers to all circumference practice questions

Practice answers - Circumference

1. C = π x d (π = 3, d = 5) so C = 3 x 5 , C = 15cm.

2. C = π x d (π = 3, d = 8) so C = 3 x 8, C = 24cm.

3. C = π x d (π = 3, d = 12) so C = 3 x 12, C = 36cm

4. C = π x d (π = 3, r = 2, d is 4) so C = 3 x 4, C = 12cm

5. C = π x d (π = 3.1, d = 6) so C = 3.1 x 6, C = 18.6 cm

6. C = π x d (π = 3.1, d = 15) so C = 3.1 x 15, C = 46.5cm

Area of a circle

The formula for the area of a circle is

Area = π x radius x radiusA = π x r x rA = π r ²

Example 1 - Area

Work out the area of a circle with radius

5cm. (Take π = 3)

5cm

Area = π r²

A = π x r x r

A = 3 x 5 x 5

A = 75cm²

Example 2 - AreaWork out the area of a circle with diameter

14cm. Answer to 3 significant figures (Take π = 3.14)

8cm

diameter = 16cm so radius is 8cm

Area = π r²

A = π x r x r

A = 3.14 x 8 x 8

A = 200.96 cm²

A = 201cm² (to 3 s.f.)

5 cm

A = (Take π =

3)

Practice 1:

Find the Area

4 cm

A = (Take π =

3)

Practice 2:

Find the Area

20 cm C =

A = (Take π =

3.14)

Practice 3:

Find the Circumference

and Area

Answers to all area practice questions

Practice answers - Area

1. A = π r ² (π = 3, r = 5) A = 3 x 5 x 5 A = 75cm²2. A = π r ² (π = 3, r = 4) A = 3 x 4 x 4 A = 48cm².3. A = π r ² (π = 3.14, d = 20 so the radius is

10cm.) A = 3 x 10 x 10 A = 300cm²

Questions

(i) The radius of a circle is 3.5 feet. Calculate the circumference of this circle. ............................................................................................................................................................................

(ii) Calculate the area of this circle............................................................................................................................................................................

(4)

Take π = 3.14

Answer

The radius is 3.5 so the

diameter is 7 feet

(i) C = π x d

C = 3.14 x 7

C = 21.98 cm

(ii) A = π r ²

A = π x r x r

A = 3.14 x 3.5 x 3.5

A = 38.465cm²

A = 38.46cm² (2dp)

(a)Calculate the area of a circle with radius 1.2 cm.

.........................................

.........................................

.........................................

(2)

(b)What is the radius of a circle with an area of 66 cm²?..........................................................................................................................

(3)

Take π = 3.14

Answer

The radius is 1.2 cm

(a) A = π r ²

A = π x r x r

A = 3.14 x 1.2 x 1.2

A = 4.5216cm²

A = 4.52cm² (2dp)

(b) A = π r ²

66 = π x r ²

66 = 3.14 x r ²

r = (66 ÷3.14)

r = 4.58cm (2dp)

a) A circle has a diameter of 7 cm.(i) Calculate the circumference of

this circle.....................................................................................................................................................................……………………………………….

(ii) Calculate the area of this circle................................................................................................................………………………………………………………………………………

(b) A plastic beaker has a height of 10 cm and a circular base of diameter 7 cm.Calculate the volume of the beaker.

......................................................

.......................................................

.......................................................

.......................................................

Take π = 3.14

Answer

The diameter is 7cm so the

radius is 3.5cm

(a)

(i) C = 3.14 x 7

C = 21.98 cm

(ii) A = π r ²

A = π x r x r

A = 3.14 x 3.5 x 3.5

A = 38.465cm²

A = 38.46cm² (2dp)

(b) V = area of cross section x h

V = 38.465 x 10

V = 384.65 cm³