1. **Problem:** The capacity of a closed cylindrical vessel of height 1 m is 15.4 L. Find the surface area of metal sheet needed to make it. 2. **Given:** - Height $h = 1$ m - Volume $V = 15.4$ L = $15.4 \times 10^{-3}$ m$^3 = 0.0154$ m$^3$ 3. **Formula for volume of cylinder:** $$V = \pi r^2 h$$ 4. **Calculate radius $r$:** $$r^2 = \frac{V}{\pi h} = \frac{0.0154}{\pi \times 1} = \frac{0.0154}{3.1416} \approx 0.0049$$ $$r = \sqrt{0.0049} = 0.07 \text{ m}$$ 5. **Surface area of closed cylinder:** $$A = 2\pi r h + 2\pi r^2$$ - Curved surface area $= 2\pi r h$ - Area of two circular ends $= 2\pi r^2$ 6. **Calculate surface area:** $$2\pi r h = 2 \times 3.1416 \times 0.07 \times 1 = 0.4398 \text{ m}^2$$ $$2\pi r^2 = 2 \times 3.1416 \times (0.07)^2 = 2 \times 3.1416 \times 0.0049 = 0.0308 \text{ m}^2$$ 7. **Total surface area:** $$A = 0.4398 + 0.0308 = 0.4706 \text{ m}^2$$ **Answer:** The metal sheet needed is approximately $0.471$ square metres.