Question

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? $[Assume\pi =\frac{22}{7}]$

Answer 1

Let the radius of the circular end be r.
Height (h) of the cylindrical vessel = 1 m
Volume of cylindrical vessel $=15.4litres=0.0154m^3$
$[Assume\pi =\frac{22}{7}]$
$\pi r^{2}h=0.0514m^3$
$(\frac{22}{7}\times r^2\times 1)m=0.0154m^3$
$\Rightarrow r=0.07m$
Total surface area of the vessel $=2\pi r(r+h)$
$[2\times \frac{22}{7}\times 0.07(0.07+1\left)\right]m^2$
$=0.44\times 1.07m^2$
$=0.4708m^2$
Therefore, $0.4708m^2$ of the metal sheet would be required to make the cylindrical vessel.