Question

A Copper wire diameter 6 mm is evenly wrapped on a cylinder of lenght 15 cm and diameter 49 cm to cover its whole surface. find the lenght and volume of wire. lf density of copper be 9 gm/cu cm find the weight of wire​

Answer 1

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$\sf{\underline{Given:}}$


$\sf{Diameter\:of\:copper\:wire}$ = $\sf{6\:mm}$

$\sf{Radius}$ = $\sf{3\:mm}$

$\sf{Length\:of\:cylinder}$ = $\sf{150\:mm}$

$\sf{Diameter\:of\:cylinder}$ = $\sf{490\:mm}$


$\sf{No.\:of\:turns\:of\:copper\:wire}$ $= \frac{150}{6} = 25$


$\sf{Length\:of\:one\:turn}$

$= 2\pi( \frac{490}{2} )$

$= 490 \times \frac{22}{7}$

$= 1540 \: mm$


$\sf{So,}$

$\sf{Total\:length\:of\:copper\:wire}$

$= 25 \times 1540$

$= 38500 \: mm$


$\sf{Therefore,}$

$\sf{Volume\:of\:copper\:wire}$

$= \pi \times (3) ^{2} \times 38500$

$= 1089000 \: mm^{3}$

$\sf{Volume}$ = 1089 $cm ^{3}$


$\sf{Specific\:gravity\:of\:wire}$ $= 9 \: kg/cm^{3}$


$\sf{Weight\:of\:wire}$

$= (1089 \times 9)$

$= 9801 \: kg$


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