Why Is Volume Excluded in My Thermal Expansion Calculation?

[FahimP]

Homework Statement

Hell people
I am stuck on this problem I solved and got the correct ans but. I somehow stumbled on the right answer by accident. My work is correct buy I have one question.

1.)
on a hot day , a cubical swimming pool is filled to within 1.9 cm of the top with water at 26 °C. When the water warms to 38 °C, the pool overflows. What is the depth of the pool? (The volume expansion coefficient for water is 2.07 10-4 °C−1.)

My question is that i accidently used B(Tf - TI ) to get the thermal expansion but the formula from the book has B V (Tf - Ti) . DO we ignore that V for volume because it is not given ? this is my question

Homework Equations

dV = BV(Tf-Ti) -- > volume expansion equation from book

The Attempt at a Solution

thermal expansion = B ( Tf-Ti)
= ( 2.07 x 10 ^ -4 ) ( 12 C ) = 0.002484
0.019 m / 0.002384 = 7.64 m
So, the depth of the pool is 7.64 m
my ans is correct

 

[p21bass]

In your attempt at a solution, you left out the volume term from the original equation. But, you seem to have ended up including it afterward. What you needed to do (and it looks like you ended up doing so) was write volume as a function of depth. Since it is a cubical pool, the original volume is d²(d-.019m), and the "final" volume (where it would overflow) is d³. If you put that on both sides of your equation - as noted in "Relevant Equations," volume/depth terms will start canceling out and you'll be left with one d. For which you ended up correctly solving.