$2\mathrm{.}11\mathrm{.}11$ A $0\mathrm{.}3$ m $-$diameter, $0\mathrm{.}6$ m long cylinder floats in an open tank containing a liquid having a specific weight $.$ A $U-$tube manometer is connected to the tank, as shown in Fig. P$2\mathrm{.}11\mathrm{.}11.$ When the pressure in pipe $A$ is $690$ Pa below atmospheric pressure, the various fluid levels are as shown. Determine the weight of the cylinder. Note that the top of the cylinder is flush with the fluid surface.

FIGURE P$2\mathrm{.}11\mathrm{.}11$