Question: The cylinder below has a radius of $4$ cm and a volume of $350$ cm$^3$. Work out the length of the cylinder. Give your answer to 2 d.p.
1. **State the problem:** We need to find the length (height) of a cylinder given its radius and volume.
2. **Formula for the volume of a cylinder:**
$$ V = \pi r^2 h $$
where $V$ is volume, $r$ is radius, and $h$ is height (length).
3. **Given values:**
- Radius $r = 4$ cm
- Volume $V = 350$ cm$^3$
4. **Rearrange the formula to solve for height $h$:**
$$ h = \frac{V}{\pi r^2} $$
5. **Substitute the known values:**
$$ h = \frac{350}{\pi \times 4^2} = \frac{350}{\pi \times 16} $$
6. **Simplify the denominator:**
$$ h = \frac{350}{16\pi} $$
7. **Calculate the numerical value:**
$$ h = \frac{350}{16 \times 3.1416} = \frac{350}{50.2656} $$
8. **Divide:**
$$ h \approx 6.960 $$
9. **Round to 2 decimal places:**
$$ h \approx 6.96 \text{ cm} $$
**Final answer:** The length of the cylinder is approximately $6.96$ cm.