Question

A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.

Answer 1

We have,

Radius of the sphere, `"R" = 18/2 = 9  "cm"` and 

Radius of the wire, `"r" = 4/2 = 2  "mm" = 0.2  "cm"`

Let the length of the wise be l.

Now,

Volume of the wire = Volume of the copper sphere 

`=> pi"r"^2"l" = 4/3 pi"R"^3`

`=> "l" = (4"R"^3)/(3"r"^2)`

`=> "l" =(4xx9xx9xx9)/(3xx0.2xx0.2)`

∴ l = 24300 cm = 243 m.