A copper rod of diameter 1 ,cm and length 8 , | vedclass

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(A) The volume of the copper rod is given by the formula for the volume of a cylinder: $V = \pi r^2 h$.Given diameter $= 1 \,cm$,so radius $r = 0.5 \,

Vedclass · Accepted Answer

$0.67$

Vedclass · Answer

(A) The volume of the copper rod is given by the formula for the volume of a cylinder: $V = \pi r^2 h$.Given diameter $= 1 \,cm$,so radius $r = 0.5 \,cm$. Length $h = 8 \,cm$.Volume $= \pi 	imes (0.5)^2 	imes 8 = \pi 	imes 0.25 	imes 8 = 2\pi \,cm^3$.When the rod is drawn into a wire,the volume remains constant.The length of the new wire is $18 \,m = 1800 \,cm$.Let the radius of the wire be $r_w$. The volume of the wire is $\pi 	imes r_w^2 	imes 1800$.Equating the volumes: $\pi 	imes r_w^2 	imes 1800 = 2\pi$.$r_w^2 = \frac{2\pi}{1800\pi} = \frac{1}{900}$.$r_w = \sqrt{\frac{1}{900}} = \frac{1}{30} \,cm$.The thickness (diameter) of the wire is $2 	imes r_w = 2 	imes \frac{1}{30} = \frac{1}{15} \,cm$.$\frac{1}{15} \,cm \approx 0.0667 \,cm = 0.67 \,mm$.

$A$ copper rod of diameter $1 \,cm$ and length $8 \,cm$ is drawn into a wire of length $18 \,m$ of uniform thickness. Find the thickness of the wire. (in $mm$)

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