A wire having diameter 3 mm.is wound about a cylinder whose length is $12 c m$ and diameter $10 c m$ , so as to cover the curved surface of the cylinder. Find the length and mass of the wire. Assume that the density of the material of the wire is $8.88$ gm per ${c m}^{3}$ ?

1256 c m, 788 g

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1256, 800 g

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1200, 788 g

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1156 c m, 769 g

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Solution

The correct option is A $1256 c m, 788 g$
$I t i s a s s u m e d t h a t o n e r o u n d o f c o p p e r w i r e w i l l c o v e r 3 m m o r 0.3 c m h e i g h t o f c y l i n d e r .$

$N u m b e r o f r o u n d s = \frac{H e i g h t o f t h e c y l i n d e r}{d i a m e t e r o f t h e w i r e}$

$= \frac{12}{0.3}$

$= 40 r o u n d s$

$N o w, T h e l e n g t h o f t h e w i r e r e q u i r e d i n o n e r o u n d = C i r c u m f e r e n c e o f t h e b a s e o f t h e c y l i n d e r$

$D i a m e t e r o f t h e c y l i n d e r = 10 c m, s o t h e r a d i u s = 5 c m .$

$c i r c u m f e r e n c e = 2 π r$

$= 2 * π * 5$

$L e n g t h o f w i r e r e q u i r e d i n o n e r o u n d = 10 π$

$L e n g t h o f w i r e r e q u i r e d i n 40 r o u n d s = 10 π * 40$

$= 400 * \frac{22}{7}$

$= \frac{8008}{7}$

$L e n g t h o f t h e w i r e = 1257.14 c m$

$R a d i u s o f t h e w i r e = \frac{0.3}{2} = 0.15 c m$

$V o l u m e o f w i r e = A r e a o f c r o s s s e c t i o n o f w i r e \times l e n g t h o f t h e w i r e$

$= π * r ² \times 12.57$

$= \frac{22}{7} \times {(0.15)}^{2} \times 1257.14$

$V o l u m e o f t h e w i r e = 88.898 c m ³$

$M a s s = D e n s i t y \times V o l u m e$

$= 8.88 \times 88.898$

$M a s s = 789.41 g m$

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A wire having diameter 3 mm.is wound about a cylinder whose length is 12cm and diameter 10cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire. Assume that the density of the material of the wire is 8.88 gm per cm3 ?

A wire having diameter 3 mm.is wound about a cylinder whose length is $12 c m$ and diameter $10 c m$ , so as to cover the curved surface of the cylinder. Find the length and mass of the wire. Assume that the density of the material of the wire is $8.88$ gm per ${c m}^{3}$ ?