Well don't worry, it's pretty simple :D
Charles' Law states that V/T= k (volume * temperature = some constant). So if you have 2 sets of volume and temperature (v1/t1=k and v2/t2=k) [v1 means v<subscript>1] then k is equal in both equations, so v1/t1 = v2/t2.
v1/t1 = v2/t2 is the equation you're going to use, and you don't need to explain where this equation comes from, you can just use it like that!
Note that you can only use kelvin for this, not celcius. K = C + 273. so:
So we have 2 sets, v1 and 21C, and v2 and 37C. so v1/21 = v2/37C.
We know that the volume of a cubical object is length*width*height (V=lwh). so:
(l1w1h1)/21 = (l2w2h2)/37
It's the same pool for the volume of water, so the l and w are the same, i.e. l1=l2 and w1=w2. so:
(lwh1)/21 = (lwh2)/37
Dividing by lw in both sides gives:
h1/21 = h2/37
Now, h2 is basically h1 with 1cm added (because it overflows). So we can say that h2 = h1+1, which means that h1 = h2-1. h2 is the actual depth of the pool. So:
h2-1/21 = h2/37
Remember to convert the 21 and 37 to kelvin, then solve!
Good luck :D
· 8 years ago