Answer to Question #184955 in Civil and Environmental Engineering for John Prats

Question

Ice has a density of 0.92 g/cm³ and seawater has a density of 1.04 g/cm³. Determine the total volume of a floating iceberg if 30 m³ is above the seawater.

Answer 1

Provided that the

Density of ice is =$0.92 g/m^3$

Density of sea water $=$ $1.04 g/cm^3$

Volume of Ice berg above water $= 30 m^3 or 3.0 \times 10^7 cm^3$

If v' is the volume of ice berg immersed in water

then as per the law of floatation = $\frac{v'}{V} = \frac{density of ice }{density of sea water}$

$=\frac{v'}{V}= \frac{0.92}{1.04}= 0.8846$

v' = 0.88361 V

Volume of the iceberg over the surface of sea water is obtained by:

V(1 - 0.8846) = $3.0 \times 10^7 cm^3$

$V = \frac{3.0 \times 10^7 cm^3}{1-0.8846} = 2.59965 \times 10^8 cm^3$

V= $259.9653 m^3$