Answer:
[tex]m=135000000 Kg[/tex]
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:
[tex]\rho=\frac{m}{V}[/tex]
where [tex]\rho[/tex] is the density, [tex]m[/tex] is the mass and, [tex]V[/tex] 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:
[tex]V= (length)(heigh)(width)[/tex].
So for our pool
[tex]V= (20)(50)(10)[/tex].
[tex]V= 10000m^{3}[/tex].
Our density is in [tex]g/mL[/tex], so the last thing we need to do before computing the mass is to express the density in [tex]Kg/m^{3}[/tex] (this is because we want our mass in [tex]Kg[/tex] and, we have our volume in [tex]m^{3}[/tex]).
For the density conversion we have to remember that
[tex]1000mL = 1L[/tex]
[tex]1L=0.001m^{3}[/tex]
[tex]1000g=1Kg[/tex]
so
[tex]\rho=13.5\frac{g}{mL}*\frac{1000mL}{1L}*\frac{1L}{0.001m^{3}}*\frac{1Kg}{1000g} =13500\frac{Kg}{m^{3}}[/tex].
With this we can finally compute mass:
[tex]\rho=\frac{m}{V}[/tex]
[tex]m=\rho*V[/tex]
[tex]m=(13500*10000) Kg[/tex]
[tex]m=135000000 Kg[/tex].
