The radius of the base and the height of a solid right circular cylinder are in the ratio 2:3 and its volume is 1617 cm3. Find the total surface area of the cylinder. [Take π = 22/7.]
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