Question

An area of `"1 hectare"` was filled to a depth of `0.1*m`, and then filled with soil whose density was `1*g*cm^-3`. What mass of soil was used?

Answer 1

`1,000*kg`

Explanation:

We must measure the volume of the plot of the land, and then multiply by the density:

`"1 hectare"` `=` `100*mxx100*m=10000*m^2`

We multiply this value by the depth, to give a volume:

`10000*m^2xx0.1*m=1000*m^3`

And we multiply this volume by the density to get the mass:

`1000*m^3xx1*g*cm^-3=1000*m^3xx1*g*(10^-2*m)^-3=`

`1000*m^3xx1*g*10^6*m^-3=`

`cancel(1000)*cancel(m^3)xx1*cancelgxxcancel(10^-3)*kg*cancel(g^-1)xx10^(cancel(6)3)*cancel(m^-3)=`

`10^3*kg`

I think this is right (all care taken, but no responsibility admitted!). It is always too easy to make an error in these sorts of calculations. We required a mass, and got a mass. Anyway, please check the calculation. Again, I suspect that the actual density of soil would be much more than `1*g*cm^-3`.