The density of Aluminum is 2.70 g/cm3. A square piece of Aluminum foil, 15.0 cm on a side, is found to weigh 2.106 g. What is the thickness of the foil in micrometers?

To determine the thickness of the aluminum foil in micrometers, we can use the relationship between mass, density, volume, and thickness.

### Step 1: Find the area of the foil.
The foil is square-shaped, so its area \( A \) can be calculated as:
\[
A = \text{side} \times \text{side} = 15.0 \, \text{cm} \times 15.0 \, \text{cm} = 225 \, \text{cm}^2
\]

### Step 2: Use the density formula to find the volume.
The density \( \rho \) of the aluminum is given as \( 2.70 \, \text{g/cm}^3 \). The mass \( m \) of the foil is \( 2.106 \, \text{g} \).

The formula for density is:
\[
\rho = \frac{m}{V}
\]
Where \( V \) is the volume. Rearranging to solve for \( V \):
\[
V = \frac{m}{\rho} = \frac{2.106 \, \text{g}}{2.70 \, \text{g/cm}^3} \approx 0.780 \, \text{cm}^3
\]

### Step 3: Relate volume to thickness.
The volume of the foil can also be expressed as:
\[
V = A \times t
\]
Where \( t \) is the thickness of the foil. Solving for \( t \):
\[
t = \frac{V}{A} = \frac{0.780 \, \text{cm}^3}{225 \, \text{cm}^2} \approx 0.00347 \, \text{cm}
\]

### Step 4: Convert the thickness to micrometers.
Since \( 1 \, \text{cm} = 10,000 \, \mu\text{m} \), the thickness in micrometers is:
\[
t = 0.00347 \, \text{cm} \times 10,000 \, \mu\text{m/cm} \approx 34.7 \, \mu\text{m}
\]

Thus, the thickness of the aluminum foil is approximately **34.7 micrometers**.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the thickness change if the mass of the foil were doubled?
2. What is the significance of the density in determining the thickness?
3. How would you calculate the thickness if the foil were not square but rectangular?
4. Can you explain why micrometers are a useful unit for measuring the thickness of materials like foil?
5. How would the result change if the density of the material was incorrectly assumed to be 3.00 g/cm³?

**Tip:** When converting units, always keep track of conversion factors to ensure accuracy.

Learn how to calculate the thickness of aluminum foil using its density and mass. This problem involves geometry, density, and volume calculations. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation