Question

A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, find its width.

Answer 1

Given:

Diameter of sphere = 8 cm

Radius of sphere $r_s$=$\frac{8}{2}$ = 4 cm = 0.04 m

Let the radius of cylinder be $r_c$ and

Length of wire(cylinder) h = 12 m

Now, The volume of sphere = Volume of cylinder

$\frac{4}{3}\pi r_s^3=\pi r_c^2\times h$
$\frac{4}{3}{r}_s^3=r_c^2\times h$
$\frac{4}{3}(0.04{)}^3=r^2\times 12$
$r^2=\frac{4\times (0.04{)}^3}{3\times 12}$
$r^2=\frac{0.000256}{36}$

$r=\frac{0.016}{6}$
r = 0.0026 m
r = 0.26 cm $(\because 1m=100cm)$

Therefore, The width of the wire = 2r
= 2 x 0.26 cm
= 0.52 cm