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

Answer:

area = 5733.33  cm²

length = 5.47 ×$10^{7}$ cm

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