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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