Circles

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# Circles - PowerPoint PPT Presentation

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.

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## PowerPoint Slideshow about 'Circles' - porter-barrera

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### 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

Circumference = π x diameter

For Example-

Area= π x 10

= 31.41592654....

= 31.4 cm (to 1 dp)

10cm

• Find the Circumference of a circles with:
• A diameter of :
• 8cm
• 4cm
• 11cm
• 21cm
• 15cm
• 6cm
• 32cm
• 18cm
• 24cm
• 50cm

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Finding the Area

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

For Example-

Area= π x 72

= π x 49

= 153.93804

= 153.9 (to 1dp) cm2

7cm

Compound Area and Perimeter

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

Find the area of the shape below:

10cm

Area of this semi circle = π r2 ÷ 2

= π x 52 ÷ 2

= π x 25÷ 2

=39.3 cm2 (1dp)

8cm

10cm

Area of this rectangle= 8 x10

=80cm2

Area of whole shape = 80 + 39.3

= 119.3 cm2

Compound Area and Perimeter

Find the perimeter of the shape below:

10cm

Circumference of this semi circle = πd ÷ 2

= π x 10÷ 2

=15.7 cm (1dp)

8cm

10cm

Perimeter of this rectangle= 8 + 8 + 10

=26cm

(don’t include the red side)

Perimeter of whole shape = 26 + 15.7

= 31.7 cm

Compound Area and Perimeter

Find the areaof the shape below:

5cm

Area of this quarter circle = π r2 ÷ 4

= π x 52 ÷ 4

= π x 25÷ 4

=19.7 cm2 (1dp)

10cm

11cm

Area of whole shape = 110+ 19.7

= 129.7cm2

Area of this rectangle

10 x 11=110

Compound Area and Perimeter

Work out all missing sides first

Find the perimeter of the shape below:

?

5cm

Circumference of this quarter circle = πd ÷ 4

= π x 10÷ 4 (if radius is 5, diameter is 10)

=7.9 cm (1dp)

6cm

5cm

10cm

10cm

11cm

Area of whole shape = 42+ 7.9

= 49.9cm

10+10 + 11+ 5 + 6= 42cm

Questions

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

2cm

3

1

2

12cm

10cm

20cm

6cm

11cm

4cm

17cm

4cm

6cm

Do not worry about perimeter here

Do not worry about perimeter here

6

4

5

10cm

10cm

5cm

5cm

5cm

20cm

12cm

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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

EXAMPLE- find the volume of this cylinder

4cm

• Find the area of the circle
• π x r2
• π x 42
• π x 16 = 50.3 cm2 (1dp)

10cm

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

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

Questions

Find the volume of these cylinders, to 1 decimal place

3

1

2

4cm

3cm

5cm

12cm

10cm

15cm

6

3cm

4

5

2cm

7cm

18cm

11.3cm

14cm

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Volume of Cylinders 2

EXAMPLE- find the height of this cylinder

4cm

• Find the area of the circle
• π x r2
• π x 42
• π x 16 = 50.3 cm2 (1dp)

h

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

50.3 x h = 140cm3

Rearrange this to give

h= 140 ÷ 50.3

h=2.8 cm

Volume= 140cm3

Volume of Cylinders

EXAMPLE- find the radius of this cylinder

r

• Find the area of the circle
• π x r2

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

π x r2 x 30 = 250cm3

94.2... x r2 = 250

Rearrange this to give

r2 = 250 ÷ 94.2

r2 =2.7 (1dp)

r= 1.6 (1dp) cm

30cm

Volume= 250cm3

Questions

Find the volume of these cylinders, to 1 decimal place

3

1

2

4cm

3cm

5cm

h

h

h

volume= 320cm3

volume= 120cm3

volume= 100cm3

5

6

r

r

r

4

12cm

8cm

14cm

volume= 90cm3

volume= 150cm3

volume= 200cm3

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Volume of Spheres

The formula for the volume of a sphere is

e.g

A= 4/3 x π x 103

A= 4/3 x π x 1000

A=4188.8 cm3 (1 dp)

10cm

Volume of Cones

The formula for the volume of a cone is

10cm

e.g

A= 1/3 x π x 42 x 10

A= 1/3 x π x 16 x 10

A=167.6 cm3 (1 dp)

4cm

Questions

Find the volume of these spheres, to 1 decimal place

3

1

2

10cm

20cm

5cm

15cm

12cm

13cm

6

4

5

3cm

9cm

4cm

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