Circles

Circles

Finding the Circumference

You can find the circumference of a circle by using the formula-

Circumference = π x diameter

For Example-

Area= π x 10 = 31.41592654.... = 31.4 cm (to 1 dp)

10cm

You can find the circumference of a circle by using the formula-

Circumference = π x diameterFor Example-

Area= π x 10 = 31.41592654.... = 31.4 cm (to 1 dp)

10cm

Find the Circumference of a circles with:1.A diameter of :

a) 8cmb) 4cmc) 11cmd) 21cme) 15cm

2.A radius of :a) 6cmb) 32cmc) 18cmd) 24cme) 50cm HOME

1a 25.1cmb 12.6cmc 34.6cmd 66.0cme 47.1cm

2a 37.7cmb 201.1cmc 113.1cmd 150.8cme 157.1cm

ANSWERS

Finding the Area

You can find the area of a circle by using the formula-

Area= π x Radius2

For Example-

Area= π x 72

= π x 49 = 153.93804 = 153.9 (to 1dp) cm2

7cm

Here we will look at shapes made up of triangles, rectangles, semi and quarter circles.

Find the area of the shape below:

10cm

8cm

10cm

Area of this rectangle= 8 x10

=80cm2

Area of this semi circle = π r2 ÷ 2= π x 52 ÷ 2= π x 25 ÷ 2=39.3 cm2 (1dp)

Area of whole shape = 80 + 39.3 = 119.3 cm2

Compound Area and Perimeter


Find the perimeter of the shape below:

10cm

8cm

10cm

Perimeter of this rectangle= 8 + 8 + 10

=26cm(don’t include the red side)

Circumference of this semi circle = πd ÷ 2= π x 10 ÷ 2=15.7 cm (1dp)

Perimeter of whole shape = 26 + 15.7

= 31.7 cm


Find the areaof the shape below:

11cm

10cm

Area of this quarter circle = π r2 ÷ 4= π x 52 ÷ 4= π x 25 ÷ 4=19.7 cm2 (1dp)

Area of whole shape = 110+ 19.7 = 129.7cm2

5cm

Area of this rectangle 10 x 11=110


Find the perimeter of the shape below:

11cm

10cm

Work out all missing sides first

Circumference of this quarter circle = πd ÷ 4= π x 10 ÷ 4 (if radius is 5, diameter is 10)=7.9 cm (1dp)

Area of whole shape = 42+ 7.9 = 49.9cm

5cm

6cm5cm

10cm

?

Add all the straight sides=10+10 + 11+ 5 + 6= 42cm

Questions

10cm

11cm

12cm

6cm

20cm

10cm

Find the perimeter and area of these shapes, to 1 decimal place

1 2 3

654

HOME

4cm

17cm

20cm

2cm

6cm

4cm

5cm

12cm

10cm

5cm5cm

Do not worry about perimeter here

Do not worry about perimeter here

ANSWERS AREA PERIMETER

1 38.1 23.42 135.0 61.33 181.1 60.84 27.3

5 129.3 47.76 128.5

Volume of Cylinders

Here we will find the volume of cylinders

Cylinders are prisms with a circular cross sections, there are two steps to find the volume

1) Find the area of the circle

1) Multiple the area of the circle by the height or length of the cylinder

Volume of Cylinders 2

1) Find the area of the circleπ x r2

π x 42 π x 16 = 50.3 cm2 (1dp)


50.3 (use unrounded answer from calculator) x 10 = 503cm3

EXAMPLE- find the volume of this cylinder

10cm

4cm

QuestionsFind the volume of these cylinders, to 1 decimal place

1 2 3

654

4cm

12cm

3cm

10cm

5cm

15cm

3cm

18cm

7cm

14cm

2cm

11.3cm

HOME

1 603.2

2 282.7

3 1178.1

ANSWERS

4 142.0

5 2155.1

6 508.9

Volume of Cylinders 2


π x 42 π x 16 = 50.3 cm2 (1dp)


50.3 x h = 140cm3

Rearrange this to giveh= 140 ÷ 50.3h=2.8 cm

EXAMPLE- find the height of this cylinder

Volume= 140cm3

4cm

h

Volume of Cylinders



π x r2 x 30 = 250cm3

94.2... x r2 = 250Rearrange this to giver2 = 250 ÷ 94.2r2 =2.7 (1dp)r= 1.6 (1dp) cm

EXAMPLE- find the radius of this cylinder

Volume= 250cm3

r

30cm

QuestionsFind the volume of these cylinders, to 1 decimal place

1 2 3

654

4cm

h

3cm

h

5cm

h

r

8cm

r

14cm

r

12cm

volume= 100cm3volume= 120cm3volume= 320cm3

volume= 200cm3 volume= 150cm3volume= 90cm3

HOME

ANSWERS1 6.42 4.23 1.34 2.35 1.86 1.9

Volume of Spheres

The formula for the volume of a sphere is

10cme.g

A= 4/3 x π x 103

A= 4/3 x π x 1000A=4188.8 cm3 (1 dp)

Volume of Cones

The formula for the volume of a cone is

10cme.g

A= 1/3 x π x 42 x 10A= 1/3 x π x 16 x 10A=167.6 cm3 (1 dp)

4cm

10cm

QuestionsFind the volume of these spheres, to 1 decimal place

1 2 3

654

HOME

20cm 5cm

12cm

4cm

13cm

3cm

15cm

9cm

1 4188.82 33510.33 523.6

ANSWERS

4 201.15 122.56 1272.3

Circle Formulae

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