Question:
The capacity of a closed cylindrical vessel of height 1 m is 15.4 liters. How many square meters of the metal sheet would be needed to make it?
Solution:
Given,
Height of the cylindrical vessel $=15.4$ litres $=0.0154 \mathrm{~m}^{3}\left[1 \mathrm{~m}^{3}=1000\right.$ litres $]$
Let the radius of the circular ends of the cylinders be 'r'
$\pi r^{2} h=0.0154 \mathrm{~m}^{3}$
$r=0.07 \mathrm{~m} \quad[\pi=31.4, h=1 \mathrm{~m}]$
Total surface area of a vessel $=2 \pi r(r+h)$
$=2(3.14(0.07)(0.07+1)) \mathrm{m}^{2}=0.4703 \mathrm{~m}^{2}$