In the manufacturing of computer chips, cylinders of silicon are cut into thin wafers that are 2.80 inches in diameter and have a mass of 2.00g of silicon. How thick (mm) is each wafer if silicon has a density of 2.33g/cm^3? (The volume of a cylinder is V=(pi)r^{2}h.)

Convert 2.80 inches to cm and take half (to find the radius), then V = pi*r^2*h.but pi*r^2 is the area; therefore, V = area*h. You can find the area from pi*r^2.

mass = volume x density. Substitute mass and density to find volume, Then substitute area into V = area*h and solve for h. That will give you thickness in cm.

To find the thickness of each wafer, we need to calculate the volume of silicon in each wafer and then use the formula for the volume of a cylinder to solve for height (thickness).

First, let's calculate the volume of silicon in one wafer:

Given:
- Diameter of wafer (d) = 2.80 inches
- Radius of wafer (r) = d/2 = 2.80/2 = 1.40 inches

We need to convert the radius from inches to centimeters since the density of silicon is given in grams per cubic centimeter.

Conversion factor: 1 inch = 2.54 cm

So, the radius (r) in centimeters = 1.40 inches x 2.54 cm/inch = 3.56 cm

Now, let's calculate the volume of the wafer using the formula for the volume of a cylinder:

V = πr^2h

Given:
- Mass of silicon (m) = 2.00 g
- Density of silicon (ρ) = 2.33 g/cm^3
- Radius of wafer (r) = 3.56 cm

We need to solve for height (h).

First, rearrange the formula for the volume of a cylinder:

V = πr^2h (divide both sides by πr^2)

h = V / (πr^2)

Now, let's substitute the given values:

h = 2.00 g / (2.33 g/cm^3 × π × (3.56 cm)^2)

Calculating the value in the parentheses:

h = 2.00 g / (2.33 g/cm^3 × 3.56^2 cm^2)

h = 2.00 g / (2.33 g/cm^3 × 12.70 cm^2)

h = 2.00 g / 32.27 g/cm^3

h ≈ 0.062 cm (rounded to 3 decimal places)

Finally, convert the thickness from centimeters to millimeters:

Thickness of each wafer ≈ 0.062 cm × 10 mm/cm ≈ 0.62 mm

Therefore, each wafer has a thickness of approximately 0.62 mm.

To determine the thickness of each wafer, we can use the equation for the volume of a cylinder, V = (π)r^2*h, where V is the volume, r is the radius, and h is the height (thickness) of the cylinder.

First, let's find the volume of the silicon in one wafer. We know that the mass of the silicon in one wafer is 2.00g, and the density of silicon is 2.33g/cm^3.

We can use the formula for density: density = mass/volume. Rearranging the formula, we can find the volume: volume = mass/density.

volume = 2.00g / 2.33g/cm^3.

Before continuing, let's convert the diameter of the wafer from inches to centimeters. Since there are 2.54 centimeters in one inch, we can convert as follows:

diameter = 2.80 inches * 2.54 cm/inch.

Now, let's find the radius of the wafer:

radius = diameter/2.

With the radius and the volume, we can rearrange the formula V = (π)r^2*h to solve for h:

h = V / [(π)r^2].

Let's plug in the values and calculate the thickness of each wafer step by step:

1. Convert the diameter from inches to centimeters:
diameter = 2.80 inches * 2.54 cm/inch.
diameter = 7.112 cm.

2. Calculate the volume of the silicon in one wafer:
volume = 2.00g / 2.33g/cm^3.
volume ≈ 0.86 cm^3 (rounded to 2 decimal places).

3. Calculate the radius of the wafer:
radius = diameter/2.
radius ≈ 3.556 cm (rounded to 3 decimal places).

4. Calculate the thickness of each wafer:
h = volume / [(π)r^2].
h ≈ 0.086 cm (rounded to 3 decimal places).

Finally, to convert the thickness from centimeters to millimeters, we can multiply by 10:

Thickness ≈ 0.086 cm * 10 mm/cm.

Therefore, each wafer has a thickness of approximately 0.86 mm (rounded to 2 decimal places).