Question

A cylindrical copper rod of diameter 1cm and length 8cm is drawn into a wire of length 18cm of uniform thickness find the thickness of the wire

Answer 1

so volume of the cylindrical rod

$\frac{22}{7}×0.5×0.5×8$

$\frac{44}{7}$

since the volume would be same but the change would be in radius and length

the length is fixed to 18 cm and radius or thickness have to change

$\frac{44}{7} = \frac{22}{7} × r^2 × 18$

$\frac{2}{18} = r^2$

$\frac{2}{2×9} = r^2$

$\frac{1}{9}= r^2$

on square root both side

$\frac{ \sqrt{1}}{ \sqrt{9}} = \sqrt{r^2}$

$\frac{1}{3} = r$

so the radius is $\frac{1}{3} cm$