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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