The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres.
Question. The capacity of a closed cylindrical vessel of height $1 \mathrm{~m}$ is $15.4$ litres. How many square metres of metal sheet would be needed to make it?

$\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$

Solution:

Let the radius of the circular end be r.

Height (h) of cylindrical vessel = 1 m

Volume of cylindrical vessel $=15.4$ litres $=0.0154 \mathrm{~m}^{3}$

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

$\left(\frac{22}{7} \times r^{2} \times 1\right) \mathrm{m}=0.0154 \mathrm{~m}^{3}$

$\Rightarrow r=0.07 \mathrm{~m}$

Total surface area of vessel $=2 \pi r(r+h)$

$=\left[2 \times \frac{22}{7} \times 0.07(0.07+1)\right] \mathrm{m}^{2}$

$=0.44 \times 1.07 \mathrm{~m}^{2}$

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

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