The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

Given :
Height (h) Of cylindrical vessel = 1 m
Volume of cylindrical vessel = 15.4 litres = 0.0154 \({m}^3\)

Let the radius of the circular end be r.

But we know that,

Volume of cylinder = \({\pi} {r}^2 h\)

Thus, we get that,

\(\Rightarrow \) \({\pi} {r}^2 h = 0.0154\) \({m}^3\)
\(\Rightarrow \) \(\frac{22}{7} × {r}^2 × 1 m \) = 0.0154 \({m}^3\)
\(\Rightarrow \) r = 0.07 m.

Also, we have,

Total surface area of vessel
= \(2 {\pi}r(r + h)\)
= \(2 × \frac{22}{7} × 0.07 (1 + 0.07)\) \({m}^2\)
= 0.44 × 1.07 \({m}^2\)
= 0.4708 \({m}^2\)

Therefore, 0.4708 \({m}^2\) of the metal sheet would be required to make the cylindrical vessel.