A hollow iron pipe is 21 cm long and has an external diameter of 8 cm. The thickness of the pipe is 1 cm and the density of iron is 8 g per cubic centimetre. What is the weight of the pipe in kilograms?

Introduction / Context:
This question combines geometry (volume of a hollow cylinder) with basic physics (mass = density * volume). The pipe is modelled as a hollow circular cylinder, where we know the external diameter, the thickness, the length, and the density of iron. We must first compute the volume of iron used and then convert that volume into mass in kilograms. This type of problem is common in aptitude tests, engineering entrance exams and technical interviews.

Given Data / Assumptions:

• Length of the pipe, h = 21 cm.
• External diameter = 8 cm, so external radius R = 4 cm.
• Thickness of pipe = 1 cm, so internal radius r = 4 − 1 = 3 cm.
• Density of iron = 8 g per cubic centimetre.
• The pipe is hollow only along its axis; the ends are open.

Concept / Approach:
The iron occupies the region between the outer cylinder and the inner cylinder. So the volume of iron is the difference between the volumes of two cylinders with the same height but different radii. The volume V of a cylinder is:
V = pi * radius^2 * height Hence, for the pipe: V = pi * (R^2 − r^2) * h. Once we know V in cubic centimetres, mass in grams is density multiplied by volume, and then we convert grams to kilograms.

Step-by-Step Solution:
External radius R = 8 / 2 = 4 cm. Internal radius r = 4 − 1 = 3 cm. Height h = 21 cm. Volume of iron V = pi * (R^2 − r^2) * h. Compute R^2 − r^2 = 4^2 − 3^2 = 16 − 9 = 7. So V = pi * 7 * 21 = 147pi cubic centimetres. Mass in grams = density * volume = 8 * 147pi = 1176pi g. Using pi ≈ 3.14, mass ≈ 1176 * 3.14 ≈ 3696 g. Convert to kilograms: 3696 g = 3.696 kg.

Verification / Alternative check:
We can quickly approximate: R^2 − r^2 = 7, V ≈ 147 * 3.14 ≈ 462 cm^3. Multiplying by density 8 gives about 3696 g, which fits well within typical rounding. Among the options, 3.696 kg matches this computed value exactly, so the answer is consistent and precise.

Why Other Options Are Wrong:
3.60 kg and 3.20 kg are too low and would result from approximating pi very roughly or miscalculating the difference of squares. Values like 36.0 kg and 36.9 kg are unrealistically large given the small dimensions of the pipe, and they would result from errors such as using centimetres as metres without proper conversion or mistakenly multiplying by 10 instead of converting to kilograms correctly.

Common Pitfalls:
A frequent mistake is to use the external radius alone, ignoring the hollow inner part, thereby overestimating the volume. Another common error is forgetting to convert the final mass into kilograms, leaving the answer in grams. Some students also calculate R − r instead of R^2 − r^2, which is incorrect for volume differences.

Final Answer:
The weight of the hollow iron pipe is 3.696 kg (approximately).