The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. Find the area of the metal sheet needed to make it.
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.
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