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

Step 1: Convert all measurements to the same unit.
The volume of silver is given in cubic centimetres: \(66 \text{ cm}^3\). The wire has a diameter of 1 mm, which is \(0.1\) cm, so its radius is \(r = 0.05\) cm.
Step 2: Use the cylinder volume formula.
The wire is essentially a long thin cylinder, so its volume is \(V = \pi r^2 L\), where \(L\) is the length in cm.
Step 3: Substitute known values.
\(66 = \frac{22}{7} \times (0.05)^2 \times L\).
Step 4: Simplify \((0.05)^2\).
\((0.05)^2 = 0.0025\), so \(66 = \frac{22}{7} \times 0.0025 \times L = \frac{0.055}{7} \times L\).
Step 5: Solve for L.
\(L = \frac{66 \times 7}{0.055} = \frac{462}{0.055} = 8400\) cm.
Step 6: Convert to metres.
\(8400\) cm \(= 84\) m, since 1 m = 100 cm. This matches option (1). The other options come from either mixing up the diameter with the radius or a units-conversion slip, so they are incorrect.