Suppose a distant world with surface gravity of $4\mathrm{.}32$ m$/$s$2$ has an atmospheric pressure of $8\mathrm{.}12104$ Pa at the surface.

$($a$)$ What force is exerted by the atmosphere on a disk$-$shaped region $2\mathrm{.}00$ m in radius at the surface of a methane ocean?

N

$($b$)$ What is the weight of a $10\mathrm{.}0-$m deep cylindrical column of methane with radius $2\mathrm{.}00$ m$?$ Note: The density of liquid methane is $415$ kg$/$m$3.$

N

$($c$)$ Calculate the pressure at a depth of $10\mathrm{.}0$ m in the methane ocean.

Pa