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The density of ice is 0.92 g cm-3 and that of sea water is 1.025 g cm-3. Find the total volume of an iceberg which floats with it's volume 800 cm3 above water.

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Answer

Given,

Density of ice = 0.92 g cm-3

Density of sea water = 1.025 g cm-3

Let total volume of iceberg be V cm3

Volume of iceberg above sea water = 800 cm3

Volume of iceberg immersed in sea water = (V - 800) cm3

By the principle of floatation,

Volume of immersed partTotal volume=Density of iceDensity of water∴(V−800)V=0.921.025⇒1.025V−820=0.92V⇒1.025V−0.92V=820⇒0.105V=820⇒V=8200.105=7809.52 cm3\dfrac{\text {Volume of immersed part}}{\text{Total volume}} = \dfrac{\text {Density of ice}}{\text {Density of water}} \\[1em] \therefore \dfrac{(V - 800)}{V} = \dfrac{0.92}{1.025} \\[0.5em] \Rightarrow 1.025V - 820 = 0.92V \\[0.5em] \Rightarrow 1.025V - 0.92V = 820 \\[0.5em] \Rightarrow 0.105V = 820 \\[0.5em] \Rightarrow V = \dfrac{820}{0.105} = 7809.52 \text{ cm}^3

Hence,

Total volume of iceberg = 7809.52 cm3

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