The diameter of a metallic sphere is 6 cm

• Mensuration

The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36 m, then what is its radius equal to?

1. 0.001 cm
2. 0.01 cm
3. 0.1 cm
4. 1.0 cm

Answer

The volume of the wire = πr²l, where r is its radius and l is its length (since the wire is cylindrical in shape)

Volume of the sphere = (4/3)πR³, where R is the radius of the sphere.

Now, R = 6/2 cm = 3 cm. So, equating the two volumes, we have 

πr²l = (4/3)πR³ 

⇨ r² × 36 × 100 = (4/3) × 3³ 

⇨ r² = (4 × 9)/(36 × 100)

= 1/100 

⇨ r = 1/10 = 0.1 cm

The correct option is C.