A volume of 88 cubic centimetres of silver is drawn into a uniform wire 1 mm in diameter. What will be the length of the wire in metres?

Introduction / Context:
This problem converts a given volume of metal into the length of a cylindrical wire of specified diameter. Such questions are common in physics and aptitude tests and rely on the volume formula for a cylinder. Because the metal is simply reshaped, its volume is conserved, so the volume of the wire equals the original volume of silver.

Given Data / Assumptions:

• Volume of silver V = 88 cm^3.
• Wire is uniform and cylindrical.
• Diameter of wire = 1 mm.
• We want wire length in metres.
• No loss of material is assumed when drawing the wire.

Concept / Approach:
The volume of a cylinder is given by:
V = π * r^2 * h, where r is radius and h is height or, in this context, wire length. We must convert the diameter from millimetres to centimetres so that all length units in the formula are consistent. Once we have r in centimetres and V in cubic centimetres, we can solve for the length h in centimetres and then convert to metres.

Step-by-Step Solution:
Step 1: Convert diameter to radius in centimetres. Diameter = 1 mm. Since 10 mm = 1 cm, 1 mm = 0.1 cm. Radius r = 0.1 / 2 = 0.05 cm. Step 2: Use cylinder volume formula V = π * r^2 * h. 88 = π * (0.05)^2 * h. Step 3: Compute r^2 = (0.05)^2 = 0.0025. So 88 = π * 0.0025 * h. Step 4: Solve for h. h = 88 / (π * 0.0025). Take π ≈ 22 / 7, so denominator ≈ (22 / 7) * 0.0025. It is easier to rewrite in fraction form: 0.0025 = 25 / 10000 = 1 / 4000. So π * 0.0025 ≈ (22 / 7) * (1 / 4000) = 22 / 28000. Then h ≈ 88 / (22 / 28000) = 88 * (28000 / 22) = 4 * 28000 = 112000 cm. Step 5: Convert centimetres to metres. 1 m = 100 cm, so h = 112000 / 100 = 1120 m? But note we must recheck: a simpler exact calculation gives h = 35200 / π cm, and with π ≈ 22 / 7, this becomes 35200 * 7 / 22 = 11200 cm. So the correct h = 11200 cm = 112 m.

Verification / Alternative check:
Using the simplified exact form directly: V = π * r^2 * h with r = 0.05 cm and V = 88 cm^3 gives h = 88 / (π * 0.0025) = 35200 / π cm. With π ≈ 3.14, h ≈ 35200 / 3.14 ≈ 11210 cm, very close to 11200 cm, confirming that 112 m is accurate when standard approximations are used.

Why Other Options Are Wrong:
84 m, 96 m, 108 m and 128 m correspond to different assumed lengths that, if substituted back into the volume formula, would not yield 88 cm^3 of silver. They therefore do not conserve the original volume and cannot be correct.

Common Pitfalls:
The main sources of error are incorrect unit conversions between millimetres, centimetres and metres, and miscalculations involving small decimal squares like 0.05^2. Some learners also forget that the radius is half the diameter. Working carefully with fractions instead of decimals often reduces arithmetic mistakes in such questions.

Final Answer:
The length of the wire is 112 metres.