Question

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

Answer 1

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{\boxed { \huge \mathcal\red{ solution}}}}$

According to the QuestionA copper rod of diameter 1 cm and length 8 cm is drawn into a wire length 18 metre of uniform thickness.

Now for the copper rod

diameter=1cm

radius=0.5 cm

length=8cm

therefore....

Volume=π(0.5)²(8) cm³

for the wire

radius=r (let)

length=18 metre=1800 cm

therefore it's volume

=π(r)²(1800)

as the rod is drawn into a wire so their volume will remain same ..

=>π(0.5)²(8)=π(r)²(1800)

=>r²=(0.5²×8)/1800

=>r=√[(0.5²×8)/1800

$= > r = \sqrt{ \frac{0.5 \times 0.5 \times 8}{1800}} \\ = > r = \sqrt{ \frac{ 5 \times 5 \times 8}{1800 \times 10 \times 10}} \\ = > r = \sqrt{ \frac{ \cancel2 \cancel{00}}{ \cancel{1800} \cancel{00}} } \\ = > r = \sqrt{ \frac{1}{900} } \\ = > r = \frac{1}{30} \\ = > \boxed { \red{r = 0.033 \: cm \:} }(approx)$

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