Question

The ratio of the radius of base to the height of a cylinder is 2 ∶ 3. If the volume of the cylinder is 1617 cm³, then what is the curved surface area of the cylinder? (Take π = 22/7)
1. 242 cm²
2. 385 cm²
3. 462 cm²
4. 770 cm²

Answer 1

Correct Answer - Option 3 : 462 cm²

Given:

r : h = 2 : 3

Volume of cylinder = 1617 cm³

Formula:

Let radius & height of the cylinder are r & h respectively. 

1. Volume of cylinder = πr²h

2. Curved surface area of cylinder = 2πrh

Calculation:

We know that,  

Volume of cylinder = πr2h

⇒ 1617 = π × r² × h

⇒ 1617 = (7/22)  × r2 × h

⇒ 1617 × (7/22) =  r2 × h

⇒ r²h = 514.5     ----(1)

But according to question,

r/h = 2/3

⇒ h = 3r/2        ----(2)

Put this value in equation (1)

r2 × (3r/2)  = 514.5

⇒ r³ = 343

⇒ r = 7 cm.

Hence, 

h = 3 × 7/2 = 21/5

⇒ h = 10.5 cm.

Hence, curved surface area 

A = 2πrh

⇒ A = 2 × (22/7) × 7 × (21/2)

⇒ A = 463 cm².

∴ The curved surface area of cylinder 462 cm².