The diameter of a solid copper sphere is 6cm. The sphere is melted and shaped into a new wire whose diameter is 0.2 cm. Then the length of wire is-

Explanation

Radius of sphere = $\frac{6}{2} = 3 cm$ Volume of sphere = $\frac{4}{3} \pi r^3$ = $\frac{4}{3} \pi (3)^3$ A solid is melted and shaped into a wire it is clear that the new shape is cylindrical. Let the length is $l$ and given that diameter = 0.2cm ∴ radius of wire = $\frac{0.2}{2} = 0.1 cm$ Logo or seal (475) ## Page 24 Volume of sphere = Volume of cylinder $$ \frac{4}{3} \pi (3)^3 = \pi (0.1)^2 l $$ $$ l = \frac{4}{3} \times \frac{27}{(0.1)^2} $$ $$ l = 3600cm, \ l = 36m $$