A $1\mathrm{.}2-$m$-$diameter, $3-$m$-$high sealed vertical cylinder is completely filled with gasoline whose density is $740$ kg$/$m$3.$ The tank is now rotated about its vertical axis at a rate of $70$ rpm$.$ Determine $($a$)$ the difference between the pressures at the centers of the bottom and top surfaces and $($b$)$ the difference between the pressures at the center and the edge of the bottom surface. $[$Ans: $2\mathrm{.}18$ kPa;$7\mathrm{.}16$ kPa$]$