Question

$1.1{cm}^3$ of gold is drawn into a wire of $0.1mm$ in diameter. Find the length of the wire of the wire in meter.

Answer 1

Volume of gold$=1.1{cm}^3$

Volume of gold$=1.1\times 1000{mm}^3=1100{mm}^3$ since $1{cm}^3=1000{mm}^3$

Diameter of the wire$=0.1$mm

Radius$=\frac{Diameter}{2}=\frac{0.1}{2}=0.05$mm

Let the length of the wire be $h$mm

Volume of wire(in the form of cylinder)$=\pi r^{2}h$

Volume of gold$=$Volume of wire

Volume of gold is melted and drawn into a wire of diameter $0.1$ mm

$1100=\frac{22}{7}\times {\left(0.05\right)}^2\times h$

$\Rightarrow h=\frac{1100\times 7}{22\times 0.05\times 0.05}$

$\Rightarrow h=\frac{77000000}{550}=140000$mm

$\Rightarrow h=\frac{140000}{1000}=140$m since $1$mm$=\frac{1}{1000}$m

Hence, the length of the wire is $140$m