Question

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

Answer 1

Height of the vessel$=1$m

Capacity of the vessel$=15.4$ liters

$=\frac{15.4}{1000}{m}^3=0.0154m^3$

Volume of the cylindrical vessel$=\pi r^{2}h=0.0154$

$\Rightarrow \frac{22}{7}\times r^2\times 1=0.0154$

$r^2=\frac{0.0154\times 7}{22}=0.0049$

$\Rightarrow r=0.07$m

Metal sheet needed to make the cylindrical vessel$=$T.S.A of the cylindrical vessel.

$\Rightarrow 2\pi r(r+h)=2\times \frac{22}{7}\times 0.07(0.07+1)m^2$

$=0.4708m^2$

$\therefore 0.4708m^2$ of sheet will be required to make the vessel.