# 1 cm3 of gold is drawn into a wire 0.1 mm in diameter.

Question:

1 cm3 of gold is drawn into a wire 0.1 mm in diameter. Find the length of the wire.

Solution:

Let r cm be the radius of the wire and h cm be the height of the wire.
Volume of the gold = 1 cm3
1 cm3 of gold is drawn into a wire of diameter 0.1 mm.

Here, $r=0.1 \mathrm{~mm}=\frac{0.1}{20} \mathrm{~cm}=\frac{1}{200} \mathrm{~cm}$

$\therefore \pi r^{2} h=1$

$\Rightarrow \frac{22}{7} \times \frac{1}{200} \times \frac{1}{200} \times h=1$

$\Rightarrow h=\frac{40000 \times 7}{22}=12727.27 \mathrm{~cm}$

Hence, length of the wire = 127.27 m