Question: User: 4
Olympic medals have a radius of $30\text{mm}$ and a thickness of $10\text{mm}$. Silver has a density of $9\text{g/cm}^3$. Find the mass of a silver medal (to 1 dp).
1. **State the problem:** We need to find the mass of a silver Olympic medal shaped like a cylinder with radius $30\text{mm}$ and thickness (height) $10\text{mm}$, given the density of silver is $9\text{g/cm}^3$.
2. **Formula used:** The mass $m$ is given by the formula:
$$m = \text{density} \times \text{volume}$$
3. **Calculate the volume of the cylinder:**
The volume $V$ of a cylinder is:
$$V = \pi r^2 h$$
where $r$ is the radius and $h$ is the height.
4. **Convert units:**
Radius $r = 30\text{mm} = 3.0\text{cm}$ (since $10\text{mm} = 1\text{cm}$)
Height $h = 10\text{mm} = 1.0\text{cm}$
5. **Calculate volume in $\text{cm}^3$:**
$$V = \pi \times (3.0)^2 \times 1.0 = \pi \times 9 = 9\pi \approx 28.2743\text{ cm}^3$$
6. **Calculate mass:**
$$m = 9 \times 28.2743 = 254.4687\text{ g}$$
7. **Round to 1 decimal place:**
$$m \approx 254.5\text{ g}$$
**Final answer:** The mass of the silver medal is approximately $254.5\text{ g}$.