Question

When an object floats in water, it displaces a volume of water that has a weight equal to the weight of the object. If a ship has a

weight of 4795 tons, how many cubic feet of seawater will it displace? Seawater has a density of 1.025 g.cm3; 1 ton = 2000 lb.
(Enter your answer in scientific notation.)

Answer 1

`\boxed{1.574 * 10^(5)\text{ ft}^(3)}`

Step-by-step explanation:

1. Mass of ship in pounds

`m = \text{4795 t} * \frac{\text{2000 lb}}{\text{1 t}} = 9.590 * 10^(6)\text{ lb}`

2. Mass of ship in kilograms

`m = 9.590 * 10^(6)\text{ lb} * \frac{\text{1 kg}}{\text{2.205 lb}} = 4.349 * 10^(6)\text{ kg}`

3. Mass of ship in grams

`m = 4.349 * 10^(6)\text{ kg} * \frac{\text{1000 g}}{\text{1 kg}} = 4.349 * 10^(9)\text{ g}`

4. Volume of water displaced

`V = 4.349 * 10^(9)\text{ g} * \frac{\text{ 1.025 cm}^(3)}{\text{1 g}} = 4.458 * 10^(9)\text{ cm}^(3)`

5. Volume of water in litres

`V = 4.458 * 10^(9)\text{ cm}^(3) * \frac{\text{ 1L}}{\text{1000 cm}^(3)}= 4.458 * 10^(6)\text{ L}`

6. Volume of water in cubic feet

`V = 4.458 * 10^(6)\text{ L} * \frac{\text{ 1 ft}^(3)}{\text{28.32 L}}= \mathbf{1.574 * 10^(5)}\textbf{ ft}\mathbf{^(3)}\\\\\text{The ship will displace } \boxed{\mathbf{1.574 * 10^(5)}\textbf{ ft}\mathbf{^(3)}} \text{ of seawater}`