Question

a copper rod of diameter 2cm and lengthy 10cm is drawn into a wire of uniform thickness and length 10m.Find the thickness of the wire.
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Answer 1

Given :

A copper rod of diameter 2cm and length 10cm is drawn into a wire of uniform thickness and length 10 m .

To Find :

Find the thickness of the wire .

Solution :

Here , we can observe that , the volume of the copper rod is equal to the volume of the copper wire .

Diameter of Copper Rod : 2 cm .

So , 2 × Radii = 2 cm .

Hence , radii of copper rod is 1 cm.

Volume Of Copper Rod :

=> Cross Sectional Area × Length

=> π • 1² × 10

=> 10π cm³ .

Volume of copper wire :

=> Cross Sectional Area × Length

Let the thickness of the wire be t cm .

So ,

=> π t² × 1000 = 10 π

=> 1000 t² = 10

=> t² = 10/1000

=> t² = 1/100

As thickness can't be negative ;

So , t is 1/10 th of a cm or 0.1 cm .

Answer :

The thickness of the wire is 0.1 cm .

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Answer 2

⛧ Required Answer -

★ In the Question it is given that , a copper rod of diameter = 2cm and lengthy = 10cm is drawn into a wire of uniform thickness and length = 10m.

★And now we need to find the thickness or we can say diameter of the wire.

So let the ,

$★ \sf volume \: of \: copper \: rod \: = V_1$

$\sf (radius ( r_1) = 1cm ,height( h_1) = 10cm)$

$★ \sf volume \: of \: uniform \: wire \: = V_2$

$\sf (radius ( r_2) = r ,height( h_2) = 10m = 10 \times 10 ^{2} cm)$

As we know , Volume of Cylinder = πr²h

Now ,

$\Longrightarrow \sf \pi \: r _1 \: ^{2} \: h_1 = \pi \: r _2 \: ^{2} \: h_2$

$\Longrightarrow \sf { \cancel{\pi}} \: r _1 \: ^{2} \: h_1 = { \cancel{\pi}} \: r _2 \: ^{2} \: h_2$

$\Longrightarrow \sf{1}^{3} \times 10 = {r}^{2} \times {10}^{3}$

$\Longrightarrow \sf{1}^{3} \times { \cancel{10}} = {r}^{2} \times {10} ^ { \cancel{3}}$

$\Longrightarrow \sf{1}^{3} = {r}^{2} \times {10} ^ {2}$

$\Longrightarrow \sf {r}^{2} = \dfrac{1}{{10} ^{2} }$

$\Longrightarrow \sf {r}^ { \cancel{2}} = \dfrac{1}{ {10}^{ \cancel{2}}}$

So ,

$\Longrightarrow \sf \dfrac{1}{10} cm = 0.1cm$

Now , Diameter or thickness = 2r

$\Longrightarrow \sf 2 × 1 \: mm \: or \:2 × 0.1 \: cm$

$\Longrightarrow \sf 2 \: mm \: or \:0.2 \: cm$

⛧ Answer -

2 mm or 0.2 cm

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Hence , A copper rod of diameter 2cm and lengthy 10cm is drawn into a wire of uniform thickness and length 10m. so the thickness or diameter of the wire will be = 2 mm or 0.2 cm .