Question

If the ratio of radius and height of cylinder is 27 : 7 and it`s volume is 176 cm³. What is the curved surface area of this cylinder?
1. 582/9 sq cm
2. 528/9 sq cm
3. 528/81 sq cm
4. 58/9 sq cm

Answer 1

Correct Answer - Option 2 : 528/9 sq cm

Given:

The ratio of radius and height = 27 : 7

Volume of cylinder = 176 cm3

Formula used:

Volume of cylinder = Πr²h

The curved surface area of cylinder = 2πrh

Calculation:

Let the radius and height of the cylinder is 27x and 7x, respectively

By using formula 

 ⇒ the volume of cylinder = (22/7) × 729x² × 7x

⇒ 176 = (22) × 729x³

⇒ 8 = 729x³

⇒ 8/729 = x³

⇒ 2/9 = x

The curved surface area of cylinder = 2πrh

⇒ 2 × (22/7) × 27x × 7x

⇒ 1188x²

Put the value of x in the above expression

⇒ The curved surface area of cylinder = 1188x2

⇒ 1188 × (4/81) = 528/9 sq cm

∴ The curved surface area of the cylinder is 528/9  sq cm