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

`m=135000000 Kg`

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=(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(g)/(mL)*(1000mL)/(1L)*(1L)/(0.001m^(3))*(1Kg)/(1000g)   =13500(Kg)/(m^(3))`.

With this we can finally compute mass:

`\rho=(m)/(V)`

`m=\rho*V`

`m=(13500*10000) Kg`

`m=135000000 Kg`.