1

4cm3cm

2cm

Volume

Ondottypaperdraw5cuboidswithvolume30cm3.

Makesurethepaperistherightwayup!

Buildthiscuboid

2

Volumeofprisms

4cm

1cm3cm

2cm

1cm

3

SurfaceArea

5cm3cm

2cm

Surfaceareais...

areaofA=

areaofB=

areaofC=

AreaofA+B+C=

Totalarea=

Findthesurfaceareaofeachofyour5cuboids.

Dimensionsofcuboidxx:

areaofA=

areaofB=

areaofC=

AreaofA+B+C=

Totalarea=

4

Vol=

SA=AB

C

Surfaceareaofcuboids

Vol=

SA=

Vol=

SA=

Vol=

SA=

5

areaofA=

areaofB=

areaofC=

AreaofA+B+C=

Totalarea=

Surfaceareaofboxes

Dimensionsofbox:

6

Volumeandsurfaceareaofprisms

22 8

Findthea)volumeb)surfacearea

7

Inyourexercisebookdrawthenetofacube. (E)

Inyourexercisebookdrawthenetofacube3cmx3cmx3cm.Finditsvolumeandsurfacearea.

(D)

Inyourexercisebookdrawthenetofacuboid3cmx4cmx5cm.Finditsvolumeandsurfacearea.

(D+)

Makethenetofacuboidwithvolume40cm3.Finditssurfacearea. (C)

Makethenetofacylinderwithvolume40cm3.Finditssurfacearea. (B)

Attachments

millieanddouglasthefight7.ppt

areaofrectanglesandtriangles.ppt

areaofparallelograms.gsp

Mensuration3VolumeofaCuboid+.ppt

Arguing over area

A Millie and Douglas production

Starring: Millie the mathematical mouse

Also starring: Douglas the guard-cow

And introducing: Lily the mathematical Labrador

Millie and Douglas are fighting

again!!!!!

They cant decide who has more land

Millies land

Douglass land

Mine is

bigger

cos it

has more

perimeter

Mine is

bigger

cos it

looks

bigger

So they call in an impartial judge to decide for them

Can you

help?

Ill try

Come with

me

Can you help the impartial judge decide who has more land?

Here are the bits of land again

6 blocks

2 blocks

3 blocks

4 blocks

And the final answer is...

Neither is bigger

because both are

12 blocks squared.

SMART Notebook

Area of triangles

To find the area of a rectangle we multiply length by width.

3cm

5cm

Area = 3 x 5 = 15 cm2

4 m

5 m

Area = 4 x 5 = 20m2

What shape do you make when you draw a diagonal through a rectangle?

What is the area of the triangle?

What about this triangle?

5 cm

10cm

Area = 1/2 of 5 x 10 = 25cm2

Why???

Because.

It is half of a rectangle

5 cm

10cm

Area = 1/2 of 5 x 10 = 25cm2

Find the area of these triangles:

6cm

4cm

4cm

10cm

Area =

cm2

Area =

cm2

= 20 cm2

= 12cm2

Now try these in your book

3cm

6cm

4cm

1cm

Area =

cm2

= 9 cm2

Area =

cm2

= 2 cm2

..and so we have a formula..

The area of a triangle = base x height halved.

We can say

Area of a triangle =

Well, now for the clever bit...

Ummm, I hear you thinking (you do think, dont you?). What about triangles that arent right angled. How can that work?

Lets look at this triangle:

Not a right angle to be seen anywhere.

Lets look at this triangle:

Watch

this

It is made up of two right angled triangles!

Lets look at this triangle:

h

a

b

And now this triangle:

h

a

b

Area =

Area =

The total area =

h

a

b

Area =

Area =

+

Which (you might have to trust

me on this one) =

And since a + b is the total base length:

h

a

b

=

2

6

3

2

4

6

2

4

10

2

1

4

2

height

base

2

h

a

2

h

b

2

)

(

h

b

a

+

2

h

base

SMART Notebook

SMART Notebook

Front face

20 cm2

60 cm3

Volume = 4 cm x 5 cm x 3 cm = 60 cm3

20 cm3

40 cm3

Volume of a Cuboid

Volume = 4 mm x 3 mm x 3 mm = 36 mm3

Volume = 2 cm x 7 cm x 6 cm = 84 cm3

36 mm3

36 mm3

84 cm3

84 cm3

Volume = 9 ft x 4 ft x 6 ft = 216 ft3

216 ft3

216 ft3

Volume l x w x h

? yards3

Volume = 2 x 8 x 4 = 64 m3

Volume = 2 x 3 x 5 = 30 cm3

Volume = 5 x 5 x 5 = 125 cm3

Volume = 2.3 x 9.6 x 5 = 110.4 mm3

Volume = 1.3 x 12 x 8.1 = 126.4 cm3

Volume = 3.1 x 3.1 x 3.1 = 29.8 cm3

Volume = 3 cm x 13 cm x 21 cm = 819 cm3

Volume = 63 = 216 cm3

Volume = 1.3 m x 1.8 m x 1.1m = 2.574m3

Volume of Compound Shapes

512 cm3

288 cm3

80 cm3

Volume = 512 + 288 + 80 = 880 cm3

Volume = 83 = 512 cm3

Volume = 12 x 3 x 8= 288 cm3

Volume = 5 x 2 x 8= 80 cm3

SMART Notebook

Page 1: cuboidsPage 2: Spot the prismsPage 3: cuboidsPage 4: Surface area and volumePage 5: sa of cuboidsPage 6: sa of harder prismsPage 7: How well are you doing?Attachments Page 1