Question
CBSEENMA9003524

The volume of a cylinder is 448π cm3 and height 7 cm. Find its lateral surface area and total surface area.

Solution

Let the radius of the base of the cylinder be r cm.
            h = 7 cm
Volume = 448straight pi cm3
rightwards double arrow space space space space space space space space space πr squared straight h equals 448 straight pi
rightwards double arrow space space space space space space space space space straight r squared straight h equals 448
rightwards double arrow space space space space space space space space space straight r squared left parenthesis 7 right parenthesis space equals space 448
rightwards double arrow space space space space space space space space space straight r squared equals 448 over 7
rightwards double arrow space space space space space space space space straight r squared equals 64
rightwards double arrow space space space space space space space space straight r equals square root of 64
rightwards double arrow space space space space space space space space straight r equals 8 space cm

therefore   Lateral surface area = 2straight pirh
          
        equals 2 cross times 22 over 7 cross times 8 cross times 7 equals 352 space cm squared
Total surface area = 2 πr left parenthesis straight h plus straight r right parenthesis

 

        equals 2 cross times 22 over 7 cross times 8 cross times left parenthesis 7 plus 8 right parenthesis
         equals 2 cross times 22 over 7 cross times 8 cross times 15
equals 5280 over 7 cm squared equals 754.28 space space cm squared.

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