Question

How deep under water must we dive for the pressure to become 6.48 times the pressure at the surface?

Answer 1

The pressure at the surface level is equal to 1 atm.

For every 10 meters underwater, the pressure increases by 1 atm.

So we can write the following equation relating the pressure P for x meters underwater:

$P=1+\frac{1}{10}x$

We want the pressure to be 6.48 times the pressure at the surface, that is, 6.48 atm.

So we have:

$\begin{gathered} 6.48=1+\frac{1}{10}x\\ \\ \frac{1}{10}x=6.48-1\\ \\ \frac{1}{10}x=5.48\\ \\ x=5.48\cdot10\\ \\ x=54.8\text{ m} \end{gathered}$

Therefore the depth underwater is 54.8 meters.