Question

If a sphere of diameter is melted 8cm and cast into wire of diameter 3 mm then find the length of the wire in meter

Answer 1

Here we have been given

Diameter of sphere = 8cm

∴ Radius = $\frac{8}{2}$

              = 4cm

For cylinderical wire,

Diameter = 3mm

∴ Radius = $\frac{3}{2}$

               = 1.5 mm = 0.15 cm

Let the length of the wire be x cm

So according to the question,

Volume of cylinderical wire = Volume of sphere

     ⇒    $\pi r^{2} h$ = $\frac{4}{3} \pi r^{3}$

     ⇒     $0.15\times 0.15\times x = \frac{4}{3}\times 4 \times4\times4$

     ⇒     $x = \frac{4\times 4\times 4\times 4}{3\times 0.15\times 0.15}$

     ⇒     $x = \frac{256}{0.0675}$

    ⇒      $x = 3792.60$ cm

    ⇒       $x = 37.926 meters$