If a ship has a mass of 10 million kilograms, what volume of fresh water must it displace in order to float? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$
A) $10 ^ { 7 } \mathrm {~m} ^ { 3 }$
B) $10 ^ { 4 } \mathrm {~m} ^ { 3 }$
C) $10 ^ { 12 } \mathrm {~m} ^ { 3 }$
D) $10 ^ { 8 } \mathrm {~m} ^ { 3 }$
E) $10 ^ { 10 } \mathrm {~m} ^ { 3 }$

Question

Quizplus · Accepted Answer

To float, the ship must displace a volume of water equal to its own mass. Using the formula for density, $\rho = \frac{m}{V}$, where $m$ is mass and $V$ is volume, and rearranging for $V$, we get $V = \frac{m}{\rho}$. Substituting $m = 10^7 \, \text{kg}$ and $\rho = 1000 \, \text{kg/m}^3$, we find $V = \frac{10^7}{1000} = 10^4 \, \text{m}^3$.

If a Ship Has a Mass of 10 Million Kilograms 1000 kg/m31000 \mathrm {~kg} / \mathrm { m } ^ { 3 }1000 kg/m3

If a Ship Has a Mass of 10 Million Kilograms $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$