Question

A solid metallic sphere of radius 4.2 cm is melted and recast into a right circular cylinder of radius 6 cm. What is the height (in cm) of the cylinder (correct to one decimal place)?
1. 1.8
2. 2.1
3. 3
4. 2.7

Answer 1

Correct Answer - Option 4 : 2.7

Given:

Radius of solid metalic sphere = 4.2 cm 

Radius of right circular cylinder = 6 cm

Formula used:

Volume of  asphere = (4/3)πr³

Volume of cylinder = πr²h 

Calculations:

After melting,

Volume of sphere = volume of cylinder

(4/3) × (22/7) × 4.2 × 4.2 × 4.2 = (22/7) × 6 × 6 × h

⇒ (4/3) × 4.2 × 4.2 × 4.2 = 36 × h

⇒ h = (4 × 4.2 × 4.2 × 4.2)/(36 × 3)

⇒ h = 2.744

Roundoff one digit = 2.7

∴ The height of cylinder is 2.7 cm