Answer:
1.63×10⁻² ft³ is the volume of sea water displaced.
Explanation:
This is the Archimedes's principle, when an object floats in water, it displaces a volume of water that has a weight equal to the weight of the object.
Let's think this formulas
mass . gravity = Weight
density . gravity = Specific weight
The formula for Archimedes's principle is:
Weight of an object = Specific weight of the liquid . submerged volume
To find out the Weight of the ship, we convert the tons to kg.
4753 tons . 1kg / 1×10⁻³ tons = 4753000 kg
gravity = 9.8 m/s²
Weight of the ship = mass . gravity → 4753000 kg . 9.8 m/s² = 46579400 N
To apply the formula, we have to convert the density to kg/m³
1.025 g/cm³ → In 1cm³ we have 1.025 g
1cm³ = 1×10⁻⁶ m³
In 1×10⁻⁶ m³ we have 1.025 g
In 1m³ we would have 1.025×10⁹ g
So 1.025×10⁹ g . 1kg/ 1×10⁻³ g = 1.025×10⁶ kg/m³
Let's go to the formula:
46579400 N = 1.025×10⁶ kg/m³ . 9.8 m/s² . Sumerged volume
46579400 N = 10045000 N/m³ . Sumerged volume
46579400 N / 10045000 m³ /N = Sumerged volume → 4.63 m³
Let's make the final conversion
4.63 m³ . 35.31 ft³ / 1m³ = 1.63×10⁻² ft³
