Question

The radius of spherical ball is one-fourth of that of cylindrical pipe while the height of cylinder is 3 times the radius of sphere. Find the ratio of curved surface area of cylindrical pipe and spherical ball.

1. 6 ∶ 1
2. 3 ∶ 2
3. 7 ∶ 5
4. 7 ∶ 2

Answer 1

Correct Answer - Option 1 : 6 ∶ 1

Given:

Radius of spherical ball is one-fourth of that of cylindrical pipe.

Height of cylinder is 3 times the radius of sphere.

Concepts used:

CSA of cylinder = 2πrh

CSA of sphere = 4π(r’)²

Calculation:

Let radius of cylindrical pipe be r units.

⇒ Radius of spherical ball (r’) = r/4 units

Height of cylinder (h) = 3 × radius of spherical ball = 3 × r/4 = 3r/4

CSA of cylindrical tool = 2πrh

⇒ 2πr × 3r/4= 3πr²/2 units

CSA of spherical ball = 4π(r’)²

⇒ CSA of spherical ball = 4π × (r/4)² = πr²/4 units

Ratio = CSA of cylindrical pipe/CSA of spherical ball

⇒ Ratio = (3πr²/2)/(πr²/4) = 6 ∶ 1

∴ Ratio of CSA of cylindrical pipe and CSA of spherical ball is 6 ∶ 1.