$(1)$ Fluid Statics: Consider a diver who has descended down $10$ meters deep.

a$.$ What is the static pressure at that depth?

b$.$ In order to breathe, the regulator attached to their air cylinders must provide at least that pressure. Assuming their air tank cylinder has an internal pressure of $200$ bar $($it $200$ atmospheres$)$ and a volume of $10$ liters, how many actual breathes can the diver take $($assume one breathe requires $0\mathrm{.}5$ L of air$)$ before running out of air?

c$.$ The human body is mostly water, with some bone and some fat, the former of which is denser than water the latter of which is less dense. The only thing that actually makes the human body buoyant though is the air in your lungs. If you exhale completely, the average density of the human body will be about $1025k\frac{g}{m^3}.$ What percentage of your total body volume will you need to inhale to float in saltwater $($density of about $1020k\frac{g}{m^3})?$