Scale Factor and the relationship
to area and volume
GLE 0706.2.3
0706.4.3
SPI: 0706.2.7
0706.4.3
Remember these rules !!
If 2number
shapesthat
arewe
The
similar,by
it is by
multiply
the
multiplication
scale
factor.
Scale factor is the ratio
of corresponding parts.
Let’s review, what we know about
similar shapes.
1.75 cm
2.8 cm
2.8 = 1.75
5.6
x
x
5.6 cm
9.8 = 2.8 x
2.8
2.8
Try again
x = 2m
8m
x
6m
6
1.5
1.5 m
= 8
x
12 = 6 x
6
6
Remember:
if shapes are similar
it is because they are
related by multiplication.
If a shape doubles, the scale
factor is 2; if the shape triples
in size, the scale factor is 3, and
so on.
1.75 cm
2.8 cm
3.5 cm
5.6 cm
The second
quadrilateral
is twice as tall
and twice
as wide.
This means the
scale factor is 2.
Scale factor and Area
1.75 cm The rule: to find
the
area
of
the
2.8 cm
second shape
The
scale factor
is 2, so
multiply
the area
its
is times
4…
ofsquare
the first
let’s
it. factor
thetest
scale
3.5 cm
squared.
5.6 cm
Since the
Remember, you
1.75 cm scale factor is 2, the
are
shape is twice as
2.8 cm
(using
l * w) scale
the scale
factor2
tall and twice as wide.
2
factor
1.75 to
x find
2.8area
x 2
when
don’t
1.75 you
x 2.8
x4=
3.5 cm know the length
19.6 cm
of 2
Check
yourself..
all the sides.
is
that
=
to
5.6 cm
5.6 x 3.5 ?
The second tripled in size, so
the scale factor is 3
The area of the second:
2
Area
of
first
x
6
4
5
15
10 x 32
10 x 9 = 90
Yes,
15if* you
12 use
= 90
Is
this½true
the formula ½ b x h
The reason this works is
because area is increased
by length and width. If both
dimensions are increased,
you are square – ing.
2m
6m
18m
2
=
3
The second shape
is 3x as big, so the
scale factor is 3.
The area of the
first times the
2
Scale factor .
12 x
=
2
12 x 9 108m
10 cm
If the scale factor is ½
what would be the
area of the smaller?
Area of the first times
2
the scale factor
10 * 10 * (1/2)2=
100 * ¼ = 25 cm2
Scale factor and volume
Now let’s look at scale factor
and volume.
The rule is to multiply the
volume of the known times
3
the scale factor .
Remember you are increasing
the length, width, and height of
a shape, thus cube - ing.
5 cm
10 cm
30 cm
The scale factor is 3, because
the size has tripled. What is the
volume of the larger prism?
3
Hint: volume of small x scale factor
150 x 33= 150 x 27 = 4050 cm3
5m
30 m
5m
10 m
What is the scale factor?
½ the
shape
is reduced
by 2
What
is the
volume
of the small?
Hint: volume of small x scale
factor3
3
3
750 x (1/2) = 750 x 1/8 =93.75 cm
Now Check yourself !!
length width Scale
factor
2
15
10
Answers:
600
3
5
3
135
20
40
1/2
200
Now Check yourself !!
length width
3
6
height Scale
factor
2
2
6
12
4
4
30
60
20
1/5
288
18432
288
Assume all the shapes are cubes