Question

An iron 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?
(4 marks)

Answer 1

Given, the diameter of iron rod = 1 $cm$
Length of the iron rod = 8 $cm$
Length of the wire = 18 $m$ = 1800 $cm$

Both, the iron rod and the wire are in the shape of cylinder and we know that the volume of a cylinder is given by $\pi \times radiu{s}^2\times h$
(0.5 marks)

Volume of the rod = $\pi r^{2}h$
$=\left(\pi \right)\times (\frac{1}{2}{)}^2\times 8=2\pi c{m}^3$
(1 mark)

Volume of the wire = $\pi r^{2}h$
$=\left(\pi \right)\times (r{)}^2\times 1800=1800\pi r^{2}c{m}^3$
(1 mark)

Iron rod is drawn into a wire of length 18 m. Here, the shape is changed but the volume remains same.

Volume of the rod (old solid shape) = Volume of the wire (New solid shape)

2$\pi =1800\pi r^2$
(0.5 marks)

$r^2=\frac{1}{900}$

r = $\frac{1}{30}$
(0.5 marks)

Diameter = $2\times \frac{1}{30}=\frac{1}{15}=0.06cm$

Therefore, thickness of the wire is 0.06 cm.
(0.5 marks)