1. **State the problem:** We have a closed cylindrical hot water tank with volume 300 litres. We want to find the height $h$ in terms of $\pi$ and $r$, and then show the total surface area formula. 2. **Volume formula for a cylinder:** The volume $V$ of a cylinder is given by $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Convert litres to cubic meters:** Since $1\text{ m}^3 = 1000$ litres, the volume in cubic meters is $$300 \text{ litres} = \frac{300}{1000} = 0.3 \text{ m}^3$$ 4. **Find $h$ in terms of $r$ and $\pi$:** Using the volume formula, $$0.3 = \pi r^2 h$$ Solve for $h$: $$h = \frac{0.3}{\pi r^2}$$ 5. **Surface area of a closed cylinder:** The total surface area (TSA) is the sum of the areas of two circular ends and the curved surface: $$\text{TSA} = 2\pi r^2 + 2\pi r h$$ 6. **Substitute $h$ from step 4 into TSA:** $$\text{TSA} = 2\pi r^2 + 2\pi r \times \frac{0.3}{\pi r^2}$$ Simplify the second term: $$= 2\pi r^2 + 2 \cancel{\pi} r \times \frac{0.3}{\cancel{\pi} r^2}$$ $$= 2\pi r^2 + 2 \times 0.3 \times \frac{r}{r^2}$$ $$= 2\pi r^2 + 0.6 \times \frac{1}{r}$$ 7. **Final formula:** $$\boxed{\text{TSA} = 2\pi r^2 + \frac{0.6}{r}}$$ This matches the given formula for the total surface area.