# Homework Help: Something in my brain has gone horribly wrong

1. Oct 26, 2007

This is an extremely easy concept that for some reason is destroying my life right now.

It just came up in a physics problem that I posted elsewhere.

I have a cube of side length .6m So the area of one side is (.6)^2=
.36m^2

This does not agree with me. If it were of side length 6 then A=6^2=36.

This makes sense. 36>6. But .36<.6

Same with volume 6^3=216>6........but .6^3=.216<.6

what gives? What the hell is wrong with me/this?

Casey

2. Oct 26, 2007

### cristo

Staff Emeritus
It's just the units that you're using. If you think of a cube of sides 60cm, then the area of one side would be 3600cm^2. Now, converting into metres; 1m^2=(100cm)*(100cm)=10,000cm^2, so 3600cm^2=3600/10000 m^2=0.36m^2.

3. Oct 26, 2007

Maybe I need to sleep on it, but I still don't see how the number of units squared can be less than the number of units in 1 dimension.

4. Oct 26, 2007

....maybe I see it now...darn, now I have NO idea what is wrong in my physics problem:yuck:

Casey

5. Oct 26, 2007

### Gokul43201

Staff Emeritus
It seems your question can be reduced to a problem with accepting that for all positive n, n > 1 => n2 > n and n < 1 => n2 < n.

Does restating your confusion in the above terms help clear some fog?

6. Oct 27, 2007

### Integral

Staff Emeritus
You are trying to compare .6m a length to .36m2 an area. This is an apples to oranges comparison, there is no way that a length can be greater then, less then, or even equal to a length.

If you would take the time to draw a picture, I bet you will quickly agree that square .6m on a side is about 1/3 of a square 1m on a side.

Last edited: Oct 27, 2007
7. Oct 27, 2007

### Gib Z

Remember, when you square it, your units also get squared. So basically before when it only took 100 cm for 1 m, now it takes 10,000 cm^2 for 1m^2.

8. Oct 27, 2007

Yeah. I kid got beef with that too. I am not sure why yet...but I do.

Did I just say got beef?

Casey

9. Oct 27, 2007

### arildno

Multiplying a number with another number that is less than 1 yields a number less than the first.

10. Oct 27, 2007

### HallsofIvy

Have you looked at a graph of y= x2 lately? For x< 1, it is below the line y= x. For x> 1, it is above. Of course, the curve and line cross at (0,0) and (1,1).