The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres.

Height of the cylinder, h = 1 m

Capacity of the cylinder = 15.4 L = 15.4 × 0.001 m3 = 0.0154 m3

$\therefore \pi r^{2} h=0.0154 \mathrm{~m}^{3}$

$\Rightarrow \frac{22}{7} \times r^{2} \times 1=0.0154$

$\Rightarrow r=\sqrt{\frac{0.0154 \times 7}{22}}=0.07 \mathrm{~m}$

∴ Area of the metal sheet needed to make the cylinder 

= Total surface area of the cylinder

$=2 \pi r h(r+h)$

$=2 \times \frac{22}{7} \times 0.07 \times 1 \times(0.07+1)$

$=2 \times \frac{22}{7} \times 0.07 \times 1 \times 1.07$

$=0.4708 \mathrm{~m}^{2}$

Thus, the area of the metal sheet needed to make the cylinder is 0.4708 m2.