Targeting Grade C

Targeting Grade CSSM 3Circles

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 circlee. 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 dC = 3.14 x 9C = 28.26cm

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

6 cm

Radius = 6cmDiameter = 12 cm (twice the radius)

C = π x dC = 3 x 12C = 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 circleThe formula for the area of a circle is

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

Example 1 - AreaWork out the area of a circle with

radius 5cm. (Take π = 3)

5cm

Area = π r²A = π x r x rA = 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 r²A = π x r x rA = 3.14 x 8 x 8A = 200.96 cm²A = 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