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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=22/7]`
Solution
Let the radius of the circular end be r.
Height (h) of cylindrical vessel = 1 m
Volume of cylindrical vessel = 15.4 litres = 0.0154 m3
`pir^2h=0.0154m^3`
`(22/7xxr^2xx1)m = 0.0154m^3`
⇒ r = 0.07 m
`"Total surface area of vessel "=2pir(r+h)`
`= [2xx22/7xx0.07(0.07+1)]m^2`
= 0.44 x 1.07 m2
= 0.4708 m2
Therefore, 0.4708 m2 of the metal sheet would be required to make the cylindrical vessel.
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