Answer :

Given: volume of cylinder = 1617 cm3


Let r be the radius of base and h be the height of cone


r:h = 2:3


r/h = 2/3


3r = 2h


h = 3r/2 …(i)


Formula: volume of cylinder = πr2h


1617 = (22/7) r2h


r2h = 514.5


Using (i) we have


r2 × (3r/2) = 514.5


3r3 = 1029


r3 = 343


r = 7 cm


h = 21/2 cm


Total surface area of cylinder = 2πr2 + 2πrh


= 2 × (22/7) × 72 + 2 × (22/7) × 7 × (21/2)


= 308 + 462


= 770 cm2


Therefore total surface area of cylinder = 770 cm2


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