Geometry HELP!!!

[astone788]

I have no idea how to do this question:

HELP!

[StumbleBum]

the scale factor (k) would be (1/3), which we raise to the power of three as its volume. So the bottom part is (1/27) of the entire volume. So then as a ratio there would be 1 part water to 26 parts air (to get the total of 27 parts) or 1:26.

[astone788]

thanks dude. I thought it might of been a scale factor question. Little did I know I was meant to convert it to volume scale factor.

[StumbleBum]

Yep, always remember when dealing with just lengths then you use the straight scale factor (k), when working with areas you square the scale factor (k^2) and when working with volumes you cube the scale factor (k^3)

[Stick]

In this case, it's also useful to set up a bit of a statement like: V(water cone) : V(air cone) - (V water cone). It just makes things a little easier.

[plato]

Yep, always remember when dealing with just lengths then you use the straight scale factor (k), when working with areas you square the scale factor (k^2) and when working with volumes you cube the scale factor (k^3)

Be careful of applying a rule such as the one here without looking at whether the same scale factor has been applied to both dimensions (length and width) for area and to all three dimensions (length, width and height) for volume.

For example, if the length of a rectangle is doubled, but not the width, the n the area is only doubled, not quadrupled.
If the length of a cube is halved, its length increased by a factor of 6 and its height remains the same, then the volume will increase by a factor of  1/2 x 6 x 1 = 3 - ie it is trebled.