Question

Calculate the number of kilograms of mercury required to fill a pool that is 20.0 m x 50.0 m x 10.0 m. The density of mercury is 13.5 g/mL.

Answer 1

Answer:

$m=135000000 Kg$

Step-by-step explanation:

To find the number of kilograms of mercury we need to find how to relate density, mass and, volume. For this we shall recall the density formula:

$\rho=\frac{m}{V}$

where $\rho$ is the density, $m$ is the mass and, $V$ is the volume.

We have the density and want to compute the mass so now we want to know the volume of the pool.

The volume of a rectangular pool is given by the fomula:

$V= (length)(heigh)(width)$.

So for our pool

$V= (20)(50)(10)$.

$V= 10000m^{3}$.

Our density is in $g/mL$, so the last thing we need to do before computing the mass is to express the density in $Kg/m^{3}$ (this is because we want our mass in $Kg$ and, we have our volume in $m^{3}$).

For the density conversion we have to remember that

$1000mL = 1L$

$1L=0.001m^{3}$

$1000g=1Kg$

so

$\rho=13.5\frac{g}{mL}*\frac{1000mL}{1L}*\frac{1L}{0.001m^{3}}*\frac{1Kg}{1000g} =13500\frac{Kg}{m^{3}}$.

With this we can finally compute mass:

$\rho=\frac{m}{V}$

$m=\rho*V$

$m=(13500*10000) Kg$

$m=135000000 Kg$.