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+(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+(1)/(10)x\\ \\ (1)/(10)x=6.48-1\\ \\ (1)/(10)x=5.48\\ \\ x=5.48\cdot10\\ \\ x=54.8\text{ m} \end{gathered}`

Therefore the depth underwater is 54.8 meters.