teach gcse maths volume of a cuboid and isometric drawing
TRANSCRIPT
Teach GCSE Maths
Volume of a Cuboid Volume of a Cuboid andand Isometric Isometric
DrawingDrawing
Teach GCSE Maths
Volume of a Volume of a Cuboid and Cuboid and
Isometric Isometric DrawingDrawing
© Christine Crisp
"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"
A line has 1 dimension, length
( but we have to ignore its thickness! )
A flat surface has 2 dimensions, length and width.
4cm
7cm
3cm
This is a 2-D rectangle:
Solid objects are 3-D but we draw them on a 2-D rectangle!
We can use isometric paper to help us draw a 3-D object.
The volume of a solid is the amount of space it takes up.Volume is measured in cubic units.
e.g. cm3, m3, mm3
1cm
1cm
1cm
This cube has a volume of 1cm3
All cubes have 6 faces,
face
12 edges
edge
The dots are 1 cm apart.verte
x
and 8 vertices.Edges we cannot see are often shown as
dotted lines.
This cube is made up of small cubes.
4cm4cm
4cm
4cm4cm
4cm
This cube is made up of small cubes.Each of the small cubes
measures 1cm by 1cm by 1cm.If we look at the plan view
( from the top ), we can see the number of cubes in each layer.
How many cubes are there in each layer?
How many cubes altogether?
Ans: There are 4 4 = 16 cubes in each layer. There are 4 layers, so there are 4 16 = 64 altogether.
The volume is 64cm3
4cm
4cmPlan view
Counting cubes is not a practical way of finding volume.
The volume of a cube can be found by multiplying:
volume = 4 4 4= 64cm3
For this cube,
We find the volume of a cuboid in the same way.
4cm
4cmPlan view
4cm4cm
4cm
Volume = length width height
e.g.1 Find the volume of the cuboid in the diagram.
volume = 6 4 3= 72cm3
Volume = length width height
Solution:
4cm
6cm
3cm
We can draw a cuboid without using isometric paper.
e.g.2 Find the volume of a cuboid measuring 2m by 1m by 50cm.
Decide with your partner which units you would use.
Solution:We must make all the
units the same, either metres or centimetres.
Using centimetres:
Volume = length width height volume = 200 100
50= 1 000 000cm3
Using metres: volume = 2 1 = 1m3
1 000 000cm3 = 1m3
So,
( 1m = 100cm )
( 50cm = ½m )
½
1m
2m
50cm
We know 100cm = 1m.
1 000 000cm3 = 1m3
Tell your partner why are there so many cm3 in 1m3.The diagram shows us the
reason.
When we change from metres to centimetres, each of the measurements is
multiplied by 100.To change from m3 to cm3 we multiply by
100100100.
1m2m
½m
100cm200cm
50cm
We know that
Volume = length width height
So, if we are given the volume, length and width, we can find the height.
We know that
Volume = length width height
So, if we are given the volume, length and width, we can find the height.
The easiest way is to find the area of the base.Then,
Height = Volume ÷ Area of the Base
So,
Volume = area height
Solution:
5 m
2 m
hVolume = 30 m3
e.g. Find the height, h, of the cuboid shown.
Area of the base = 2 5 = 10 m2
Height = Volume ÷ Area of the Base
So, height = 30 ÷10= 3 m
If we are given the area of the base instead of the length and width, we have less work to do !
SUMMARY Volume is measured in cubic units such as
cm3, m3 and mm3.
When we find volume, the units must all be the same. • Units
: 1m =
100cm1cm =
10mm To change from m3 to cm3 we multiply by 100 100 100.
( centimetres are smaller so we have more of them ) To change from cm3 to m3 we
divide by 100 100 100.
For a cuboid,
Height = volume ÷ area of the base
Volume = length width height
EXERCISE
1. Find the volumes of the following solids:
Solutions:(a) Volume = 3 3
3
Volume = length width height Reminder: We
can write this as 33.
= 27cm3
(b) Volume = 5 4 3 =
60cm3
Here we must write cm3 NOT 273.
3cm
(a) Cube
(b) Cuboid
5cm
4cm
3cm
EXERCISE
2. Find the height of the cuboid with length 9
cm, width 7 cm and volume 189 cm3:
Solution:
= 189 ÷ 63 = 3 cm
Height = volume ÷ area of the base
Area of base = 9 7 = 63 cm3
9cm
7cm
h
