8.5 A volumes of enlargements



Invoegen plattegrond op niveau
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Slide 1: Slide
WiskundeMiddelbare schoolhavoLeerjaar 2

This lesson contains 11 slides, with interactive quiz and text slides.

time-iconLesson duration is: 50 min

Items in this lesson



Invoegen plattegrond op niveau

Slide 1 - Slide

Today
You understand what happens to the volume of a figure when it's enlarged and are able to perform calculations accordingly.

Slide 2 - Slide

Consider these two cubes.


Slide 3 - Slide

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:



222=8
121212=1728

Slide 5 - Slide

The volumes of the cubes are:



Now,

So the volume has 
increased 216 fold
with k = 6.
222=8
121212=1728
81728=216

Slide 6 - Slide

With a scale factor of 6,
the volume is multiplied by 216.

These numbers are related:

63=216

Slide 7 - Slide

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 k3.





63=216

Slide 8 - Slide

When a 3D figure is enlarged by a factor k,
its volume is increased by a factor k3.

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 - Slide

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 - Slide

Practice!

31, 33, 35, 37
40, 42, 46, 50
53, 56, 61, 63
64, 67, 69, 70

timer
10:00

Slide 11 - Slide