The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder?

The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder? Correct Answer 4312√6

We have,

⇒ Total Surface Area/Curved Surface Area = 5/2

Let r be the radius of cylinder

⇒ Total Surface Area = Curved Surface Area + 2 × πr²

⇒ 1 + {(2 × π × r²) / (Curved Surface Area)} = 5/2

⇒ (2 × π × r²) / (Curved Surface Area) = 3/2

Also, Curved Surface Area = 2 × π × r × h

⇒ (2 × π × r²) / (2 × π × r × h) = 3/2

⇒ r = 1.5h

⇒ Total Surface Area = (2 × π × r × h) + (2 × π × r²)

On Substituting r = 1.5h, we get

⇒ 3080 = 3πh² + 4.5πh²

⇒ 3080 = 7.5 × 22/7 × h²

⇒ h = 14√(2/3) = 14√6/3

⇒ Volume = πr²h = 2.25πh² × h = (2.25) × (1232/3) × (14√6/3) = 4312√6 cm³