Question
If a cargo ship has a mass of 90,000,000 kg, how much water would it need to displace in order to float?
Group of answer choices
90,000,000,000 m3
90,000 m3
300,000 m3
200,000 m3
Group of answer choices
90,000,000,000 m3
90,000 m3
300,000 m3
200,000 m3
Answers
GPT-4o mini
To float, a ship must displace a volume of water equal to its weight. The weight of the cargo ship can be calculated using the formula:
\[
\text{Weight} = \text{mass} \times g
\]
where \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \text{m/s}^2 \). However, for the purpose of this problem, we can use the mass directly, since we can consider \( g \) is effectively 1 when dealing with the equivalent displacement volume in cubic meters of water.
The weight of the water displaced is equal to the weight of the ship. The density of water is about \( 1000 \, \text{kg/m}^3 \), so to find the volume of water displaced:
\[
\text{Volume} = \frac{\text{mass}}{\text{density}}
\]
Substituting in the values:
\[
\text{Volume} = \frac{90,000,000 \, \text{kg}}{1000 \, \text{kg/m}^3} = 90,000 \, \text{m}^3
\]
Therefore, to float, the cargo ship would need to displace **90,000 m³** of water.
The correct answer is: **90,000 m³**.
\[
\text{Weight} = \text{mass} \times g
\]
where \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \text{m/s}^2 \). However, for the purpose of this problem, we can use the mass directly, since we can consider \( g \) is effectively 1 when dealing with the equivalent displacement volume in cubic meters of water.
The weight of the water displaced is equal to the weight of the ship. The density of water is about \( 1000 \, \text{kg/m}^3 \), so to find the volume of water displaced:
\[
\text{Volume} = \frac{\text{mass}}{\text{density}}
\]
Substituting in the values:
\[
\text{Volume} = \frac{90,000,000 \, \text{kg}}{1000 \, \text{kg/m}^3} = 90,000 \, \text{m}^3
\]
Therefore, to float, the cargo ship would need to displace **90,000 m³** of water.
The correct answer is: **90,000 m³**.