A copper rod of 1 cm diameter and 8 cm length is drawn into a wire of uniform diameter and 18 m length. The radius (in cm) of the wire is,

### Concept & Conservation of Volume When a solid is reshaped, drawn, or melted into a new form, its total volume remains constant. Both the rod and the wire are cylinders. $$ V = \pi \times r^2 \times h $$ ### Step-by-Step Solution * Given rod details: diameter = 1 cm ($r_1 = 0.5 \text{ cm}$), length ($h_1$) = 8 cm. * Volume of the rod = $\pi \times (0.5)^2 \times 8 = \pi \times 0.25 \times 8 = 2\pi \text{ cm}^3$. * Given wire details: length ($h_2$) = 18 m = 1800 cm. Let the radius be $r_2$. * Volume of the wire = $\pi \times r_2^2 \times 1800$. * Equating the volumes: $\pi \times r_2^2 \times 1800 = 2\pi$. * $r_2^2 = \frac{2}{1800} = \frac{1}{900}$. * $r_2 = \sqrt{\frac{1}{900}} = \frac{1}{30} \text{ cm}$. ### Exam Strategy & Shortcut Always keep $\pi$ as a symbol; do not multiply it out. Immediately convert the 18 meters to 1800 cm to match the rod units. Then setup the equation $0.5^2 \times 8 = r^2 \times 1800$ to solve rapidly. ### Common Pitfall Failing to convert the length of the wire from meters to centimeters before equating the volumes, leading to an incorrect magnitude. ### Final Answer Therefore, the correct answer is **$\frac{1}{30}$**.