In the manufacturing of computer chips, cylinders of silicon are cut into thin wafers that are 3.00 in. in diameter and have a mass of 1.50 g of silicon. How thick, in millimeters, is each wafer if silicon has a density of?

Question: In the manufacturing of computer chips, cylinders of silicon are cut into thin wafers that are 3.30 inches in diameter and have a mass of 1.50 g of silicon. How thick (mm) is each wafer if silicon has a density of 2.33 g/cm 3 ? (The volume of a cylinder is V=πr 2 h )

Explanation:

The volume of a cylinder is

Volume V = πr^2h ....1

The density of a material is

Density D = mass m / volume V

D = m/V ....2

Since m and D are given, we can make V the subject of formula.

V = m/D ....3

From equation 1, we need to derive the thickness h of the cylindrical silicon.

h = V/πr^2 .....4

Substituting equation 3 into 4

h = (m/D)/πr^2 .....5

Given.

mass m = 1.50g

density D = 2.33g/cm^3

radius r = diameter/2 = 3.00in/2 = 7.62/2 cm = 3.81cm

Substituting the given values into the equation

h = (1.5/2.33)/(π ×3.81^2)

thickness h = 0.014cm