Question

Gold, which has a mass of 19.32 g for each cubic centimeter of volume, 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 33.16 g, is pressed into a leaf of 3.000 µm thickness, what is the area of the leaf? m2 (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 1.000 µm, what is the length of the fiber? m

Answer 1

area = 5733.33 cm²

length = 5.47 ×
`10^(7)` cm

Step-by-step explanation:

Given data

density = 19.32 g/cm³

mass = 33.16 g

thickness = 3.000 µm = 3 ×
`10^(-4)` cm

radius r = 1.000 µm = 1 ×
`10^(-4)` cm

to find out

area of the leaf and length of the fiber

solution

we know volume formula that is

volume = mass / density

volume = 33.16 / 19.32

volume = 1.72 cm³

we know that volume = thickness × area

so area

area = volume / thickness

area = 1.72 / 3 ×
`10^(-4)`

area = 5733.33 cm²

and

we know volume = πr²L

so L = volume / πr²

length = 1.72 / π(1×
`10^(-4)`)²

length = 5.47 ×
`10^(7)` cm