Question

a cooper rod of diameter 1 cm and length 8cm is drawn into a wire of length 18 m of uniform thickness .

find the thickness of the wire.

Answer 1

Hey

Here is your answer,

Given,

Diameter of the copper wire = 1 cm

Radius of the copper wire = 1 / 2 cm = 0.5 cm

Length of the copper rod = 8 cm

Volume of the cylinder = ∏×r2×h∏×r2×h
= ∏×0.52×10∏×0.52×10 …………………………………….. (i)

Length of the wire = 18 m = 1800cm

Volume of the wire = ∏×r2×h∏×r2×h
= ∏×r2×1800∏×r2×1800 …………………………………………. (ii)

Now equating both the equations. We get,

r2 = 200.00044

r= 0.033 cm

The radius or thickness of the wire is 0.033 cm

Hope it helps you!

Answer 2

$\bigstar{\pmb{\huge{\underline{\mathfrak{\red{Answer}}}}}}$

For the copper rod : R = $\sf{\frac{1}{2}cm,H=8cm}$

For the copper wire : r = ?, h = 18m = 1800cm

Volume of copper wire = Volume of copper rod

= $\sf{\pi {r}^{2} \times 1800 = \pi \times \frac{1}{2} \times \frac{1}{2} \times 8}$

= $\sf{{r}^{2} = \frac{1}{900} = {( \frac{1}{30} )}^{2}}$

$\therefore$ $\sf{r = \frac{1}{30} cm}$

Hence, the diameter of cross - section or thickness of the wire

= $\sf{\frac{1}{15}cm=\frac{1}{15}×10mm}$

= $\sf{0.67mm(approx.)}$