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23 September, 02:17

Because gasoline is less dense than water, drums containing gasoline will float in water. suppose a 240-l steel drum is completely full of gasoline. part a what total volume of steel can be used in making the drum if the gasoline-filled drum is to float in fresh water?

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  1. 23 September, 02:44
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    Since the density of gasoline is not given, let us suppose it is 750 kg/m3 and the density of steel is 7800 kg/m3.

    There are 2 constraints: 1. volume of steel + volume of gasoline = volume of water and at the threshold of sinking, 2. mass of steel + mass of gasoline = mass of water

    240L * 1m³ / 1000L = 0.240 m³

    first: Vs + Vg = Vw = Vs + 0.240m³

    second: ρs*Vs + ρg*Vg = ρw*Vw → substitute for Vw, Vg and all the densities

    7800*Vs + 750*0.240 = 1000 * (Vs + 0.240) (7800 - 1000) * Vs = 240 - 750*0.240 Vs = 60 / 6800 = 0.00882 m³ = 8.82 L ≈ 9 L
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