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Probability

Question
CBSEENMA9003521

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?

Solution
h = 1 m
Capacity = 15.4 litres = fraction numerator 15.4 over denominator 1000 end fraction space straight m cubed
                                = 0.0154 m3
Let the radius of the base be r m. Capacity = 0.0154 m3
rightwards double arrow space space space space space space space space space space space space space space πr squared straight h space equals space 0.0154
rightwards double arrow space space space space space space space space space space space 22 over 7 cross times straight r squared cross times 1 equals 0.0154
rightwards double arrow space space space space space space space space space space space straight r squared equals fraction numerator 0.0154 cross times 7 over denominator 22 end fraction
rightwards double arrow space space space space space space space space space space space straight r squared equals 0.0049
rightwards double arrow space space space space space space space space space space space straight r space equals space square root of 0.0049 end root
rightwards double arrow space space space space space space space space space space space straight r space equals space 0.07 space straight m
                              
∴ Curved surface area = 2 πrh plus 2 πr squared
equals 2 cross times 22 over 7 cross times 0.07 cross times 1 plus 2 cross times 22 over 7 cross times left parenthesis 0.07 right parenthesis squared
= 0.44+0.0308=0.4708 m2
Hence, 0.47 m2 of metal sheet should be needed.