Question

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

• A. 84
• B. 90
• C. 168
• D. 336

Hint:

Treat the wire as a thin cylinder, use volume = pi times radius squared times length, and be careful converting the diameter to the radius in the same unit as the volume.

Answer 1

The Correct Option is A

This can also be solved by keeping every length in millimetres throughout, avoiding decimals until the very last step.

1. The diameter of the wire is 1 mm, so the radius is $r = 0.5$ mm.
2. The volume of silver is $66$ cm$^3$. Since $1$ cm $= 10$ mm, $1$ cm$^3 = 1000$ mm$^3$, so $66$ cm$^3 = 66000$ mm$^3$.
3. Using the cylinder volume formula $V = \pi r^2 L$ with everything in mm: $66000 = \frac{22}{7} \times (0.5)^2 \times L$.
4. Compute $(0.5)^2 = 0.25$, so $66000 = \frac{22}{7} \times 0.25 \times L = \frac{5.5}{7} \times L$.
5. Solve for $L$: $L = \frac{66000 \times 7}{5.5} = \frac{462000}{5.5} = 84000$ mm.
6. Convert back to metres: since $1$ m $= 1000$ mm, $L = \frac{84000}{1000} = 84$ m.

Working entirely in millimetres gives the same length as the centimetre-based method.

\[\boxed{84 \text{ m}}\]