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Answer :

Given that,

Diameter of cylinder = 10 cm

So, radius of the cylinder (r) \( \frac{10}{2} \) cm

= 5 cm

Length of wire in completely one round

\( = \ 2 \pi r \ = \ 2 × \ 3.14 \ × \ 5 \ = \ 31.4 \) cm

It is given that diameter of wire = 3 mm \( = \ \frac{3}{10} \) cm

The thickness of cylinder covered in one round = \( \frac{3}{10} \) m

Hence, the number of turns(rounds) of the wire to cover 12 cm will be \( = \ \frac{12}{ \frac{3}{10}} \ = \ 12 \ × \ \frac{10}{3} = 40 \)

Now, the length of wire required to cover the whole surface = length of wire required to complete 40 rounds

\(\Rightarrow 40 \ × \ 31.4 \ = \ 1256 \) cm

Radius of the wire \( = \ \frac{0.3}{2} \ = \ 0.15 \) cm

Volume of wire = Area of cross-section of wire × Length of wire

\( = \ \pi(0.15)^2 \ × \ 1257.14 \ = \ 88.898 \) cm^{3}

We know,

Mass = Volume × Density

\( = \ 88.898 \ × \ 8.88 \ = \ 789.41 \) gm

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