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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?

Q : 6     The capacity of a closed cylindrical vessel of height 1 m is \small 15.4 litres. How many square metres of metal sheet would be needed to make it?
 

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(Using capacity(volume), we will find the radius and then find the surface area)

The capacity of the vessel = Volume of the vessel =\small 15.4 litres

Height of the cylindrical vessel = h = 1\ m

Let the radius of the circular base be r \ m

\therefore The volume of the cylindrical vessel = \pi r^2 h

\\ \Rightarrow \frac{22}{7}\times r^2 \times1 = 15.4\ litres= 0.0154\ m^3 \\ \Rightarrow r^2 = \frac{0.0014\times11\times7}{22} \\ \Rightarrow r^2 = \frac{7\times7}{10000} \\ \Rightarrow r = \frac{7}{100}= 0.07\ m

Therefore, the total surface area of the vessel = 2\pi r h+ 2\pi r^2 = 2\pi r(r+h)

\\ = 2\times\frac{22}{7}\times0.07\times(0.07+1) \\ = 0.44 \times 1.07 \\ = 0.4708\ m^2

Therefore, square metres of metal sheet needed to make it is 0.4708\ m^2 

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