

Meaning and models  Key ideas
 Length and Perimeter 
 Area  Volume and Capacity
 Mass 
Meaning
and models quiz answers
1. 
Kilo means 1000. There are 1000 m in 1 km

2. 
Micro means a millionth.
1
microsecond = one millionth of a second
therefore,
1 000 000 microseconds = 1 second

3. 
(a)
You would use length measure to measure the length of a table.
Use metres for a large table.
(b)
You would use litres to measure volume.
(c)
You would use length measure to measure the length of a baby.
Use centimetres.
(d)
You would use time units to measure the time to run 100 m. Use
seconds.
(e)
You would use mass units to measure the mass of a large dog.
Use kilograms.

4. 
Strictly
speaking, only the second is an SI unit out of those given in
the answers, therefore D. For more information read the meaning
and models section. 
5. 
Neither
is heavier. 1 kg is 1 kg no matter what you are weighing.

Key
Ideas quiz answers
1. 
1400
metres = 1400 ÷ 1000 km = 1.4 kilometres (we are converting
a smaller unit to a larger unit so we divide)



2. 
2.637
kilograms = 2.637 x 1000 g = 2637 grams (we are converting a larger
unit to a smaller unit so we multiply)



3. 
4.5
kilolitres = 4.5 x 1000 litres = 4500 litres



4. 
Check
your own answer



5.

Length of desk = 15.5 lots of 9
= 15.5 x 9
155 x 9 = 1395
so 15.5 x 9 = 139.5
Length of desk = 139.5 cm

6. 
Matthew’s measurement appears to be more accurate as he has
measured to the nearest hundredth of a centimetre, while Naomi
has measured to the nearest tenth of a centimetre. However in
most circumstances it would be unlikely that Matthew could accurately
measure to the nearest hundredth of a centimetre  this is 10
times smaller than a millimetre.

7. 
(a)
385 centimetres = 385 ÷ 100 = 3.85 metres

(b)
9.35 kilograms = 9.35 x 1000 = 9350 grams

(c)
49 millilitres = 49 ÷ 1000 = 0.049 litres

(d)
0.054 km = 0.054 x 1000 = 54 metres =
54 x 100 = 5400 centimetres

(e)
8647
km = 8647 x 1000 = 8 647 000 metres 

8. 
Number
of centimetres in 3 m 65 cm
= 300 cm + 65 cm
= 365 cm

9. 
Length of Martin’s stride = 80 cm
Length
of 60 strides = 60 x 80 = 4800 cm
Number
of m = 4800 ÷ 100 = 48 m

10. 
How
many 25 g in 1000 g?
1000
÷ 25 = 40
Number
of 25 g packets = 40

11. 
9.00pm
to 7.00am is 10 hours.
60
minutes in 1 hour
Number
of minutes in 10 hours = 10 x 60 = 600
60
seconds in 1 minute
Number
of minutes in 600 minutes = 600 x 60
= 36 000s

12. 
There are 1000 ml in a litre
So
0.325 l = 325 ml
Hence,
3250 ml is larger.

Length
and perimeter quiz
answers
1. 
a)
39 cm is 390 mm




b)
543 m = 543 x 100 cm = 54300 cm




c)
16790 mm = 16790 ÷ 10 (to get into cms) ÷ 100 (to
get into m) = 16.790 m




d)
1.44 km = 1.44 x 1000 (to get into m) x 100 (to get into cm) x
10 (to get into mm) = 1.44 x 1 000 000 = 1440 000 mm



2. 
a)
340 mm = 34 cm
34 cm < 45 cm 
b)
5009 m = 5.009 km
5.009
km < 12 km





c)
7000 mmm = 7 m
7
m < 8.5 m

d)
13 000 mm = 13 m
13
m < 1.3 km



3. 


Shape
1: Perimeter = 2.5 + 2 x 7 + 2 cm = 18.5 cm


Shape
2: Perimeter = 5 + 5 + 4.5 m = 14.5 m


Shape
3: Perimeter =
2 x 3.14 x 2.7 = 16.96
NOTE that we have used 3.14 as an estimate for pi and that our
answer has no units because we were given none in the question. 


4. 
We
are told that the radius of a swimming pool is 1.5 metres. To
find the perimeter of a circle, also called the circumference,
we use the formula, circumference .
circumference
of the pool = 2 x 3.14 x 1.5 = 9.42 metres



5. 
I
have estimated that my palm is about 10 cm wide, which is about
right for a man.
The
length of the table is 18 palm widths which is approximately
18 x 10 cm = 180 cm or 1.8 m
The width of the table is 12 palm widths which is approximately
12 x 10 cm = 120 cm or 1.2 m
When
I actually measured my palm width I realised that it was only
8.5 cm wide. Therefore a more accurate measurement of the dimensions
of the table would be:
The
length of the table is 18 palm widths which is approximately
18 x 8.5 cm = 153 cm or 1.53 m
The width of the table is 12 palm widths which is approximately
12 x 8.5 cm = 102 cm or 1.02 m
These
measurements are not exact as there would be some inaccuracy
in using my palm as a tape measure.



6. 
The
length of a small suburban house block is 36.5 m and the width
is 15.9 m.
The
perimeter of a rectangular object can be found using the formula,
Perimeter

=
2 x length + 2 x width 

=
2 x 36.5 m + 2 x 15.9 m 

=
73 + 31.8 m 

=
104.80 m 
Therefore
the perimeter of the block is 104.80 m.
The
new subdivided block will still be 36.5 m long but will only
by 7.95 m (15.9 m divided by 2) wide.
Perimeter

=
2 x length + 2 x width 

=
2 x 36.5 m + 2 x 7.95 m 

=
73 + 15.9 m 

=
88.9 m 
Therefore
the perimeter of the new block is 88.9 m.
(It
is worth noting that in an example such as this, the area of
the new blocks will be half that of the original block, but
the perimeter is not. Can you see why?)

Area quiz
answers
1. 


The
first shape is a trapezium. A = 1/2 x (a + b) x h, where 'a'
and 'b' are the bases and 'h' is the perpendicular height.
Area

=
1/2 x (a + b) x h 

=
1/2 x (2 cm + 2.5 cm) x 7 cm 

=
1/2 x 4.5 cm x 7 cm 

=
15.75 cm^{2} 
The
second shape is a triangle. A = 1/2 x b x h, 'b' is the base
and 'h' refers to the perpendicular height.
Area

=
1/2 x b x h 

=
1/2 x 4.5 cm x 3 cm 

=
6.75 cm^{2} 


NOTE:
The 'h' in the formula to calculate the area of a triangle ALWAYS
refers to the perpendicular height.
The
third shape is a circle. A
where we have used 3.142 as an approximation for 'pi' and 'r'
refers to the radius.
Area



=
3.142 x (2.7 cm)^{2} 

=
22.91 cm^{2} (rounded to 2 decimal places) 



2. 
The
area of a circle is measured by .
In this case we are told the radius is 4.5 cm
Area



=
3.142 x (4.5 cm^{2}) 

=
3.142 x 20.25 cm^{2} 

=
63.63 cm^{2 }(rounded to 2 decimal places) 



3. 
The
area of a parallelogram = base x perpendicular height
Area

=
base x height 

=
12 cm x 3.4 cm 

=
40.8 cm^{2} (rounded to 2 decimal places) 



4. 
To
find the area of the bench we will first find the area of the
circle and the the area of the rectangular portion.
We
can see that both centimetres and metres have been used as units
of measure. I will convert the centimetres to metres so that
all measurements are in the same units and there is no room
for error when we add the areas at the end.
80
cm = 0.8 m
Area
of the circle:
Area



=
3.142 x (0.8 m^{2}) 

=
3.142 x 0.64 m^{2} 

=
2.01 m^{2} (rounded to 2 decimal places) 
Area
of the rectangle:
Area

=
length x width 

=
2.3 m x 1 m 

=
2.3 m^{2} 
Adding
the two areas together, 2.01 m^{2} + 2.3 m^{2 }=
4.31 m^{2}.
So
the approximate area of the bench is 4.31 m^{2}. Note
that this is only an approximation because we can see that one
end of the rectangular bench has been overlapped by the circle.



5. 
The
tops of the desks are trapezium shaped. The formula to calculate
the area of a trapezium is 1/2 x (a + b) x h where a and b are
each side lengths.
As
we have measurements in centimetres and metres we will convert
all measurements to metres.
Area

=
1/2 x (b + a) x h 

=
1/2 x (1.1 m + 0.85 m) x 0.7 m 

=
0.68 m^{2} (rounded to 2 decimal places) 
There
are 12 desks so the total area of the tops of the desks if they
are all jammed up together is 12 x 0.68 = 8.16 m^{2}.
Therefore
all 12 desks will not fit into a 8 m^{2} square room
unless they are stacked on top of one another. 10 desks would
fit into the room, taking up 6.8 m^{2 }of space but
there would still not be much extra room.



6. 
Although
the 3 parallelograms are of different sizes, they all have the
same height of 1.8 m. (We note that the height does not have
to be vertical, but it must be perpendicular to the base).
Area1

=
1.8 m x 0.25 m = 0.45 m^{2} 
Area2

=
1.8 m x 0.48 m = 0.86 m^{2} 
Area3

=
1.8 m x 2.3 m = 4.14 m^{2} 
The
total area that requires a nonslip coating is 5.45 m^{2}.

Volume
and capacity quiz
answers
1. 
The
first solid is a cylinder. It has a uniform crosssection, so
this means we can use the formula for the volume of a prism
to its volume, V = A x h.
The
base of the prism is a circle. The formula to find the area
of a circle is, A ^{}.
Therefore the formula to find the volume of the cylinder is,
V
Volume
of a cylinder



=
3.142 x 9 cm^{2 }x 7.5 cm 

=
212.085 cm^{3} 
The
second solid is a rectangular prism. Because a prism has a uniform
crosssection we can find its volume by multiplying the area
of its base by its height. V = A x h.
Volume
of a prism

=
A x h 

=
6 cm^{2 }x 10 cm 

=
60 cm^{3} 

2. 
This
cube is also a rectangular prism. We are told the side length
of its cubic base is 4 m. So, first we will find the area of
its base.
To
find the area of a square (the cubic base) we simply multiply
its length by its length, which in this case is 4m. Therefore
the area of the base is 16 m^{2}.
To
find the volume we apply the formula to find the volume of a
prism.
Volume
of a prism

=
A x h 

=
16 m^{2} x 8 m 

=
128 m^{3} 

3. 
This
solid is also a prism, so we can use the same formula to find
its volume.
Volume
of a prism

=
A x h 

=
9 cm^{2 }x 5 cm 

=
45 cm^{3} 



Mass
quiz
answers
1. 
a)
There are 1000 kilograms in 1 tonne.


b)
1 mL of water is equivalent to 1 cm3 of water. (See Volume and
Capacity measurement facts)


c)
There are 1000 mg in 1 g.


d)
There are 1000 mg in 1g and there are 1000 g in 1 kg. So, there
is 1000 x 1000 mg in 1 kg which is 1 000 000 mg.



2. 
a)
car  use tonnes or kilograms


b)
book  use grams or kilograms (depending on how heavy the book
feels)


c)
computer  use kilograms


d)
person  use kilograms


e)
cup of flour  grams


f)
feather  milligrams



3. 
See
explanation at the beginning of this section.



4. 
a)
150 g flour, 100 g coconut, 200 g sugar, 300 g mixed fruit
150 + 100 + 200 + 300 = 750 g in total mass.




b)
25 students weigh on average 45 kilograms.
The
students estimated total mass in kilograms is 25 x 45 kg = 1125
kg
The
students estimated total mass in tonnes is 1125 kg divided by
1000, which is 1.125 t.



