Question

A solid sphere of radius $1$cm is melted to stretch into a wire of length $100$cm. Find the radius of the wire.

Answer 1

Sphere $\to r=1$cm
Wire is a cylinder
Cylinder$\to h=100cm,r=?$
Volume of sphere$=$Volume of wire(cylinder)
$\frac{4}{3}\pi r_s^3=\pi r_{cy}^2{h}_{cy}$
$r_{cy}^2=\frac{\frac{4}{3}\pi r_s^3}{\pi h_{cy}}=\frac{4r_s^3}{3\times h_{cy}}=\frac{4\times 1\times 1\times 1c{m}^3}{3\times 100cm}=\frac{1}{75}c{m}^2$
$r_{cy}=\sqrt{\frac{1}{75}}=\frac{1}{5\sqrt{3}}cm=0.11cm$
$\therefore$ Radius of the wire$=0.11$cm.