Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a)if a sample of gold with a mass of 7.583 g, is pressed into a leaf of 3.061 μm thickness, what is the area (in m2) of the leaf? (b)if, instead, the gold is drawn out into a cylindrical fiber of radius 2.500 μm, what is the length (in m) of the fiber?

(a) First of all, let's convert the gold's density into appropriate units:

and the mass as well:

From density and mass, we can find the volume of the leaf, V:

We know that the thickness is , and the volume is the product between the thickness and the area: , so we can find the area:


(b) The radius of the cylinder is , therefore its area is

For a cylinder, the volume is the product between the length L and the area A: V=AL, therefore we can find the length L (the volume is the one calculated at the previous step):