Fluids Question

[gravity falls]

A ship passes an iceberg in the Atlantic Ocean. Only 30 m3 of the iceberg is visible above the ocean water. If the specific gravity (SG) of the Atlantic is 1.020, and that of ice is 0.920, what is the total volume of the iceberg?

A.270 m3

B.300 m3

C.330 m3

D. 360 m3


The Correct Answer is 300 m^3.

I got 306 m^3, but I wanted to check with others and see how you guys did the question.

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[gettheleadout]

For floating objects, the fraction of the object volume submerged is equal to the ratio of the object density to the fluid density (derivation here). We aren't given object (iceberg) and fluid (Atlantic water) densities, but specific gravities. Specific gravity is the ratio of the density of a substance to the density of water at standard thermodynamic conditions (1 atm, 298 K). When we set up the ratio of the iceberg and ocean water specific gravities, the density of standard water cancels:

Where p_rel is specific gravity,

(p_rel iceberg) / (p_rel Atlantic) = (d_iceberg / d_H2O) / (d_Atlantic / d_H2O) = d_iceberg / d_Atlantic

That is the ratio we want, so we sub in the specific gravities given: d_iceberg / d_Atlantic = (p_rel iceberg) / (p_rel Atlantic) = 0.920 / 1.020

0.920 / 1.020 is approximately 0.9 / 1, so 90% of the iceberg's volume will be submerged. With 30 m^3 exposed, that leaves 9*30 m^3 = 270 m^3 submerged. Total iceberg volume is 30 + 270 = 300 m^3.

Edit: the temperature of the reference water actually varies; sometimes ~ 277 K is used.