The diameter of a copper sphere is 18cm. It is melted and drawn into a

1.	The diameter of a copper sphere is 18cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108m, find its diameter.
Answer» It is given that Diameter of the sphere = 18cm Radius of the sphere = 18/2 = 9cm Length of the wire = 108m = 10800 cm We know that πr²h = 4/3 πr³ By substituting the values (22/7) × r² × 10800 = 4/3 × (22/7) × 9³ On further calculation r² = (4/3 × (22/7) × 729)/ ((22/7) × 10800) So we get r² = (4 × 243)/ 10800 = 9/100 By taking square root on the RHS r = 3/10 = 0.3 cm Diameter = 2 (0.3) = 0.6 cm Therefore, the diameter of the wire is 0.6cm.

The diameter of a copper sphere is 18cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108m, find its diameter.

Answer»

It is given that

Diameter of the sphere = 18cm

Radius of the sphere = 18/2 = 9cm

Length of the wire = 108m = 10800 cm

We know that

πr²h = 4/3 πr³

By substituting the values

(22/7) × r² × 10800 = 4/3 × (22/7) × 9³

On further calculation

r² = (4/3 × (22/7) × 729)/ ((22/7) × 10800)

So we get

r² = (4 × 243)/ 10800 = 9/100

By taking square root on the RHS

r = 3/10 = 0.3 cm

Diameter = 2 (0.3) = 0.6 cm

Therefore, the diameter of the wire is 0.6cm.