Math question for all you smart guys
 

This seems like it should be easy to me but I'm not so sure now.

If one cubic yard is 3 ft x 3 ft x 3 ft, what are the dimensions of a cube whose volume is 10 cubic yards. I thought it would be 30 ft x 30 ft x 30 , but that would one 2700 yards. Where am I going wrong.

I'm afraid my ignorance is showing, but it wouldn't be the first time...

27 cubic ft x 10 = 270 cubic ft.

rjp

10 cubic yards?

1yd = 3ft
so...
10³yd = 30³ft

30³ft = X • X • X

Try it that way.

It is the cube root of 270. Get your calcumalator out.

I'm just doing this in my head while drinking. but wouldn't 9 sq' on the bottom.middle and top equal 27sq'. Not yards.

6.46 ft x 6.46 ft x 6.46 ft = 270 ft^3 = 10 yds ^3

Oh I got it now. You were right about the 30 by 30 by 30. Except you forgot those were ' and used yards instead.I'm guessing 30 x30 x 30 '.Not yards.

It's 2700 sq' not yards.

Winner! Winner! Chicken Dinner!!!

So these are the exterior dimensions? I think you're right but it just seems too small since its 10 times mores than 3 x 3 x 3!

oops. my mistake. I meant cubic ' not sq'.

This is exactly why the SI-metric system is so much easier.

1 cubic yard is 27sq'.
Im thirsty.

not really, this is one example where SI is just about the pretty much the same task.

1 x 1 x 1 = 1 cubic whatever

So what sides does a cube with 10 cubic meter volume have?

it ain't 10, and it aint 1 either..

3.16227766 meter
EDIT CRAP, and even that is wrong.

so much for metric..

Cube root of 10 = approx. 2.15

Units don't matter.

2.15 yards = +/- 6.XX feet.

2.15^3 = 10

Thats how I did it.

Yep, calculate first then convert the units.

Volume is proportionate to the cube of the linear dimension, so the cube doesn't have to get 10X "bigger" (each side's length) to have 10X the volume. That's why if you took a gazelle and scaled it up to be as big as an elephant, it's legs would break. It's mass is proportional to the volume (cube) but the strength of its leg bone is proportional to the cross sectional area (square). As you scale up the gazelle, mass increases faster than bone strength and the legs break.

Yes. Surface to weight ratio, a driving force of nature. That's why ants are so strong, proportionally.