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The question asks to calculate the mass of a gold medal, which has a diameter of 6 cm, a thickness of 1 cm, and gold's density is given as 19 g/cm³.

### Step-by-step solution:

1. **Volume of the medal**:
   The medal is shaped like a cylinder, so we can use the formula for the volume of a cylinder:
   
   \[
   V = \pi r^2 h
   \]
   where:
   - \( r \) is the radius of the base (half of the diameter),
   - \( h \) is the height or thickness of the cylinder,
   - \( \pi \) is approximately 3.1416.

   For this medal:
   - Diameter = 6 cm, so radius \( r = 6/2 = 3 \) cm,
   - Thickness \( h = 1 \) cm.

   Therefore, the volume is:

   \[
   V = \pi (3^2) \times 1 = \pi \times 9 \times 1 = 9\pi \, \text{cm}^3 \approx 28.274 \, \text{cm}^3
   \]

2. **Mass of the medal**:
   We use the density formula to calculate the mass:

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

   The density of gold is given as 19 g/cm³, and the volume we just calculated is approximately 28.274 cm³. So,

   \[
   \text{Mass} = 19 \, \text{g/cm}^3 \times 28.274 \, \text{cm}^3 \approx 537.21 \, \text{g}
   \]

Thus, the mass of the gold medal is approximately **537.21 g** (to 2 decimal places).

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Would you like more details on any step? Here are some related questions:

1. How do we calculate the volume of other 3D shapes?
2. What is the significance of density in real-world applications?
3. How is the formula for the volume of a cylinder derived?
4. What are some other examples of items with known densities?
5. How does gold's density compare with other metals?

**Tip:** Always remember to convert units when dealing with different measurements (e.g., cm to m) in complex problems.

Olympic medals have a diameter of 6 cm and a thickness of 1 cm. Gold has a density of 19 g/cm³. Work out the mass of a gold medal (to 2 decimal places).

Learn how to calculate the mass of a gold Olympic medal given its dimensions and gold's density. This problem explores geometry concepts like the volume of a cylinder and applies the density formula for calculating mass. Suitable for Grades 8-10.

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