Question: Cylinder: The water tank has the following dimensions $H = 2000\text{mm}$, $D = 1000\text{mm}$. You have been asked to work out the area of the cylinder. Provide your answer in $m^2$ and write down your formula you used. Show your workings (what did you enter into your calculator). Answer (including unit of measure).
1. **State the problem:** We need to find the surface area of a cylinder with height $H = 2000\text{mm}$ and diameter $D = 1000\text{mm}$. We will convert dimensions to meters for the final answer in $m^2$.
2. **Formula for surface area of a cylinder:**
$$ A = 2\pi r^2 + 2\pi r h $$
where $r$ is the radius and $h$ is the height.
3. **Convert dimensions to meters:**
$$ H = 2000\text{mm} = \frac{2000}{1000} = 2\text{m} $$
$$ D = 1000\text{mm} = \frac{1000}{1000} = 1\text{m} $$
Radius $r = \frac{D}{2} = \frac{1}{2} = 0.5\text{m}$.
4. **Calculate the area of the two circular bases:**
$$ 2\pi r^2 = 2 \times \pi \times (0.5)^2 = 2 \times \pi \times 0.25 = 0.5\pi $$
5. **Calculate the lateral surface area:**
$$ 2\pi r h = 2 \times \pi \times 0.5 \times 2 = 2\pi $$
6. **Total surface area:**
$$ A = 0.5\pi + 2\pi = 2.5\pi $$
7. **Numerical value:**
$$ A = 2.5 \times 3.1416 = 7.854 \text{ m}^2 $$
**Answer:** The surface area of the cylinder is approximately $7.854\text{ m}^2$.