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8.5 A volumes of enlargements
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Slide 1:
Diapositive
Wiskunde
Middelbare school
havo
Leerjaar 2
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Slide 1 - Diapositive
Today
You understand what happens to the volume of a figure when it's enlarged and are able to perform calculations accordingly.
Slide 2 - Diapositive
Consider these two cubes.
Slide 3 - Diapositive
What is the scale factor?
A
6
B
36
C
2
D
3
Slide 4 - Quiz
Consider these two cubes.
The volumes of the cubes are:
2
⋅
2
⋅
2
=
8
1
2
⋅
1
2
⋅
1
2
=
1
7
2
8
Slide 5 - Diapositive
The volumes of the cubes are:
Now,
So the volume has
increased 216 fold
with k = 6.
2
⋅
2
⋅
2
=
8
1
2
⋅
1
2
⋅
1
2
=
1
7
2
8
8
1
7
2
8
=
2
1
6
Slide 6 - Diapositive
With a scale factor of 6,
the volume is multiplied by 216.
These numbers are related:
6
3
=
2
1
6
Slide 7 - Diapositive
With a scale factor of 6,
the volume is multiplied by 216.
When a 3D figure is enlarged by a factor k,
its volume is increased by a factor k
3
.
6
3
=
2
1
6
Slide 8 - Diapositive
When a 3D figure is enlarged by a factor k,
its volume is increased by a factor k
3
.
This statement can be reversed. If the volume of the enlargement is p times as big, the scale factor is the cube root of p:
Slide 9 - Diapositive
This statement can be reversed. If the volume of the enlargement is p times as big, the scale factor is the cube root of p:
So when we know a drum holds a 1000 times as much water compared to a smaller drum, the scale factor is
Slide 10 - Diapositive
Practice!
31, 33, 35, 37
40, 42, 46, 50
53, 56, 61, 63
64, 67, 69, 70
timer
10:00
Slide 11 - Diapositive
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