66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be

### Concept & Volume of a Wire A drawn wire is mathematically modeled as a cylinder. Its volume remains constant during the drawing process. $$ V = \pi \times r^2 \times h $$ ### Step-by-Step Solution * Given: Volume $V = 66 \text{ cm}^3$. * Wire diameter = 1 mm = 0.1 cm. Therefore, radius $r = 0.05 \text{ cm} = \frac{1}{20} \text{ cm}$. * Let the length of the wire be $h$ cm. * Volume = $\frac{22}{7} \times (\frac{1}{20})^2 \times h = 66$. * $\frac{22}{7} \times \frac{1}{400} \times h = 66$. * $h = \frac{66 \times 7 \times 400}{22} = 3 \times 7 \times 400 = 8400 \text{ cm}$. * Convert length to meters: $8400 \text{ cm} = 84 \text{ m}$. ### Exam Strategy & Shortcut Convert dimensions to a common unit (cm) immediately. Use fractions like $\frac{1}{20}$ instead of $0.05$ to make manual multiplication and cancellation much faster. ### Common Pitfall Forgetting to convert the final answer from centimeters back into meters as asked in the question. ### Final Answer Therefore, the correct answer is **84**.