I read that there is enough of gold layering the surface of planet Earth with 45cm layer of gold.
My question is: Suppose that our planet is a sphere(without mountains and stuff), then how much kilograms of gold is on "Earth"?
(I now that the volume of gold is: $V=V_l-V_E$, where: $V_l=\frac{4}{3}\pi (r+45)^3$ and $V_E=\frac{4}{3}\pi r^3$ )
On
Where did you read that? The estimated gold mined till now is about 150 000 tons that is a cube with edges of length 20 meters. This will be 8000 $m^3$.
If we use the calculation in your exercise with the earth equtorial radius ($6.3781370\cdot 10^6$ m) the volume would be about $2.3 \cdot 10^{14} \, m^3$ which is about $3\cdot 10^{10}$ times more than it should be (that factor is higher than world population). That would make about $4\cdot 10^{17}$ kilograms of gold. That is about 1 percent of the amount of salt in the oceans.
Hint: Gold has a density of about $19\frac{\mathrm g}{\mathrm{cm}^3}$. Multiply this with the number of $\mathrm{cm}^3$ you find.