66 text{ cm}^3 of silver is drawn into a wire | vedclass

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(A) The volume of the silver wire is given as $V = 66 	ext{ cm}^3$. Since the wire is cylindrical,its volume is $V = \pi r^2 L$,where $r$ is the radi

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$84$

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(A) The volume of the silver wire is given as $V = 66 	ext{ cm}^3$. Since the wire is cylindrical,its volume is $V = \pi r^2 L$,where $r$ is the radius and $L$ is the length. The diameter of the wire is $1 	ext{ mm} = 0.1 	ext{ cm}$,so the radius $r = 0.05 	ext{ cm}$. Substituting the values: $66 = \pi 	imes (0.05)^2 	imes L$. $L = \frac{66}{\pi 	imes 0.0025} = \frac{66 	imes 7}{22 	imes 0.0025} = \frac{3 	imes 7}{0.0025} = \frac{21}{0.0025} = 8400 	ext{ cm}$. Converting to metres: $8400 	ext{ cm} = 84 	ext{ m}$.

$66 \text{ cm}^3$ of silver is drawn into a wire $1 \text{ mm}$ in diameter. The length of the wire in metres will be

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