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?
 

Answers (1)

(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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