scale factor and the relationship to area and volume gle 0706.2.3 0706.4.3 spi: 0706.2.7 0706.4.3
TRANSCRIPT
Scale Factor and the relationship to area and volume
GLE 0706.2.30706.4.3
SPI: 0706.2.70706.4.3
Remember these rules !!
If 2 shapes are similar, it is by multiplication
The number that we multiply by is the scale factor.
Scale factor is the ratio of corresponding parts.
Let’s review, what we know about similar shapes.
2.8 cm
x
5.6 cm
1.75 cm
2.8 1.75=x5.6
9.8 = 2.8 x2.82.8
x = 3.5cm
Try again
6 m
x
1.5 m
8 m
6 8=x1.5
12 = 6 x66
x = 2m
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
3.5 cm
2.8 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
3.5 cm
2.8 cm
5.6 cm
The rule: to find the area of the second shape multiply the area of the first times the scale factor squared.
The scale factor is 2, so its square is 4…let’s test it.
1.75 cm
3.5 cm
2.8 cm
5.6 cm
Since the scale factor is 2, the shape is twice as tall and twice as wide.
(l * w) scale factor2
1.75 x 2.8 x 22
1.75 x 2.8 x 4 =
19.6 cm 2
Check yourself.. is that = to 5.6 x 3.5 ?
Remember, you are using the scale factor to find area when you don’t know the length of all the sides.
The second tripled in size, so the scale factor is 3
45
6
15
The area of the second:Area of first x
10 x 32 10 x 9 = 90
Is this true if you use the formula ½ b x h
2
Yes, ½ 15 * 12 = 90
The reason this works is because area is increased by length and width. If both dimensions are increased, you are square – ing.
6m
18m
2m The second shape is 3x as big, so the scale factor is 3.
The area of the first times theScale factor 2.12 x 32 =
12 x 9 = 108m2
10 cmIf the scale factor is ½ what would be the area of the smaller?
Area of the first times the scale factor2
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 the scale factor3.
Remember you are increasing the length, width, and height of a shape, thus cube - ing.
10 cm3 cm
5 cm
30 cmThe scale factor is 3, because the size has tripled. What is the volume of the larger prism?
Hint: volume of small x scale factor3
150 x 33= 150 x 27 = 4050 cm3
10 m5 m
5 m30 m
What is the scale factor?
Hint: volume of small x scale factor3
750 x (1/2)3= 750 x 1/8 = 93.75 cm3
½ the shape is reduced by 2What is the volume of the small?
Now Check yourself !!
length width Scale factor
15 10 2
3 5 3
20 40 1/2
Answers:
600
135
200
Now Check yourself !!
Answers:
28818432288
length width height Scale factor
3 6 2 2
6 12 4 4
30 60 20 1/5
Assume all the shapes are cubes