or
'Why There Are No Giant Spiders!
Giant creatures the stuff of many science
fiction movies ... from giant ants and spiders to 10storey tall babies.
But is it really possible for creatures to be so large? If so, why
aren't there any 6 metre tall spiders?
On this page we'll try to explain why
ants and spiders could never be as big as an elephant ... and still
look the same.
The reason for this has to do with
scale factors ... 
Here's a simple box. Beside it is one twice as big.
You can tell it's
twice as big because we've put a scale beside it.
Actually, to be more
precise, the second box is twice as long as the first one.
The correct way to
say this is that it has been scaled up by a factor of two.
By making the box
twice as long, we've also doubled the width and height.
Here's the same diagram, only this
time we've shaded one face.
The second box is still twice as long
as the first one.
Notice what happens to the area of
one face of the box when it's twice as long ...
The AREA has been increased by a
factor of FOUR. 
Here's the same diagram again, only
this time we've shaded all the boxes.
The second box is still twice as long
as the first one.
Notice what happens to the volume of
the box when it's twice as long ...
The VOLUME has been increased by
a factor of EIGHT. 
Increasing
the length of an object by a factor of 2 increases the area by
a factor of 4 and the volume by a factor of 8.
Let's start over with
another set of boxes.
Here's a simple box.
Beside it is one three times as big.
You can tell it's
three times as big because we've put a scale beside it.
To be more precise,
the second box is three times as long as the first one.
The correct way to
say this is that it has been scaled up by a factor of three.
By making the box
three times as long, we've also tripled the width and height.
Here's the same diagram, only this
time we've shaded one face.
The second box is still three times
as long as the first one.
Notice what happens to the area of
one face of the box when it's three times as long ...
The AREA has been increased by a
factor of NINE. 
Here's the same diagram again, only
this time we've shaded all the boxes.
The second box is still three times
as long as the first one.
Notice what happens to the volume of
the box when it's three times as long ...
The VOLUME has been increased by
a factor of TWENTYSEVEN. 
Increasing
the length of an object by a factor of 3 increases the area by
a factor of 9 and the volume by a factor of 27.
Do you see the pattern?
Let's summarize what happened (and add a few more examples) in a table:

LENGTH 
AREA 
VOLUME 
Scale Factor 2 
2 times 
4 times 
8 times 
Scale Factor 3 
3 times 
9 times 
27 times 
Scale Factor 4 
4 times 
16 times 
64 times 
Scale Factor 5 
5 times 
25 times 
125 times 
Scale Factor X 
X times 
X^{2} times 
X^{3} times 
Increasing
the length of an object by factor X increases the area by factor X^{2}
and the volume by factor X^{3}
And what does all
of this have to to with giant spiders? Move on to Page
Two to find out!
