Solve the following problems and write your solutions clearly, showing all the work necessary for your solution. A correct solution without supporting work may receive little or no credit.

SITUATION $(1-2)$: An iceberg $(sg=0\mathrm{.}92)$ floats in salt water $(sg=1\mathrm{.}02).$ If $500m^3$ of ice is above the water surface. Determine the following:

If $500m^3$ of ice is above the water surface, what is the total volume of ice, in $m^3$

If the total volume of ice in $8200m^3,$ how many $m^3$ of ice is above the water surface?

SITUATION $(3-5)$: A piece of wood floats in water with $50$ mm projecting above the water surface, and when placed in a glycerin of

sp$.$gr$.1\mathrm{.}35,$ the block projects $75$ mm above the liquid surface. Determine the following:

$3.$ Height of the piece of wood.

$4.$ Specific gravity of the wood.

$5.$ Weight of the wood if it has a cross$-$sectional area of $200mm200mm.$

SITUATION $(6-9)$: For the concrete gravity dam shown, $B=4\mathrm{.}2m,b=0\mathrm{.}6m,H=7m,$ and $h=6m.$ Unit weight of the concrete is $24k\frac{N}{m^3}.$ Considering $1-$meter length of dam. Determine the following:

$6.$ Total force exerted by water on the dam.

$7.$ Resisting moment.

$8.$ Factor of safety against sliding if the coefficient of friction at the base of the dam is $0\mathrm{.}25.$

SITUATION $(9-10)$: The force acting per length of the dam shown are as follows:

$9.$ What is the factor of safety against sliding if the coefficient of friction at the base of the dam is $0\mathrm{.}25?$

$10.$ Determine the minimum bearing pressure at the base of the dam