Thermodynamics expansion problem

[xnitexlitex]

Homework Statement

On a hot summer day, a cubical swimming pool is filled to within 1.2 cm of the top with water at 24 °C. When the water warms to 34 °C, the pool overflows. What is the depth of the pool? (The volume expansion coefficient for water is 2.07 10-4 °C−1.)

Homework Equations

ΔV = βV₀ΔT

The Attempt at a Solution

I set ΔV equal to 1.2, plugged the numbers in, got 193.24 cm³ for the volume, and took the cube root of the result for the depth. That didn't work. What am I supposed to do?

 

[I like Serena]

Hi xnitexlitex!

ΔV is not equal to 1.2.
1.2 cm is the change in depth, not the change in volume.

How did you plug your numbers in and get your volume?
Because I see no reason why you would need to take a cube root...

 

[xnitexlitex]

Thank you. I just got the answer now.