Calculate the density using the following data in kg/m3. Convert to kg and meters.
1) mass 3.8g
2) length 6.4 cm
3) diameter 1.22 cm

To calculate the density, we need to use the formula:

\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]

Given:
- Mass = 3.8 g (we'll convert this to kg)
- Length = 6.4 cm (we'll convert this to meters)
- Diameter = 1.22 cm (we'll convert this to meters)

**Step 1: Convert mass, length, and diameter to standard units:**
- \( 1 \, \text{g} = 0.001 \, \text{kg} \)
  \[
  \text{Mass} = 3.8 \, \text{g} = 3.8 \times 10^{-3} \, \text{kg} = 0.0038 \, \text{kg}
  \]
- \( 1 \, \text{cm} = 0.01 \, \text{m} \)
  \[
  \text{Length} = 6.4 \, \text{cm} = 6.4 \times 10^{-2} \, \text{m} = 0.064 \, \text{m}
  \]
  \[
  \text{Diameter} = 1.22 \, \text{cm} = 1.22 \times 10^{-2} \, \text{m} = 0.0122 \, \text{m}
  \]
  The radius \( r \) is half of the diameter:
  \[
  \text{Radius} = \frac{0.0122}{2} = 0.0061 \, \text{m}
  \]

**Step 2: Calculate the volume of the cylinder:**

The volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
Where:
- \( r \) is the radius (0.0061 m)
- \( h \) is the length (0.064 m)

Substitute the values:
\[
V = \pi (0.0061)^2 (0.064)
\]

**Step 3: Calculate the density:**

Finally, the density \( \rho \) is:
\[
\rho = \frac{\text{Mass}}{\text{Volume}} = \frac{0.0038}{V}
\]

Let me calculate these values.import math

# Given data
mass = 3.8e-3  # mass in kg
length = 0.064  # length in meters
radius = 0.0122 / 2  # radius in meters

# Step 2: Calculate the volume of the cylinder
volume = math.pi * radius**2 * length

# Step 3: Calculate the density
density = mass / volume
densityThe density of the cylinder is approximately \( 507.92 \, \text{kg/m}^3 \).

Would you like more details on any of these steps or clarifications?

Here are 5 related questions to expand your understanding:
1. How does the shape of an object affect its volume calculation?
2. What other geometric shapes could you use to calculate volume and density?
3. How would you calculate the density of an irregularly shaped object?
4. How does temperature affect the density of materials?
5. What are the units commonly used for density in different contexts?

**Tip:** Always ensure the units are consistent when calculating physical quantities to avoid errors.

Learn how to calculate density using given mass (3.8g), length (6.4 cm), and diameter (1.22 cm) by converting units to kilograms and meters. This detailed step-by-step solution applies the formula for the volume of a cylinder and calculates density in kg/m³. Suitable for high school students (Grades 9-12).

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