Question

Diameter of a metallic sphere is 6 cm. By melting it an another circular wire is recasted. If the length of wire is 36 m, find its radius.

Answer 1

Given,

Diameter of sphere = 6 cm

Radius of sphere (r) = \(\frac { 6 }{ 2 }\) = 3 cm

Volume of metallic sphere = \(\frac { 4 }{ 3 }\)πr³

= \(\frac { 4 }{ 3 }\) × π × (3)³ cm³

Let the radius of the wire be R.

According to question

Length of wire = 36 m = 3600 cm.

∴ Volume of wire = πR²h.

π × R² × 3600 cm³

Again according to question

Volume of sphere = volume of wire

Hence radius of the wire = 0.1 cm.