A conical tent is erected by the army at a base camp. The tent has height 3 m and base diameter 10 m. If each person requires 3.92 cubic metres of air space, approximately how many persons can be accommodated inside the tent?

Introduction / Context:
This question uses the volume of a right circular cone to model the air space inside a conical tent. The tent dimensions are given, along with the air space required per person. By finding the total internal volume and dividing by the volume needed per person, we can estimate how many people can be seated inside the tent. This is a practical application of the cone volume formula in a real-world style scenario.

Given Data / Assumptions:

• Height of the conical tent, h = 3 m.
• Base diameter = 10 m, so radius r = 5 m.
• Volume required per person = 3.92 m^3.
• The tent is completely filled up to its full volume by air and people.
• We are asked for an approximate number of persons.

Concept / Approach:
The volume V of a right circular cone is given by:
V = (1/3) * pi * r^2 * h First compute the total internal volume of the tent using this formula. Then, to find how many persons can be accommodated, divide the total volume by the volume required per person. Because the answer must be a whole number of people, we pick the nearest suitable integer based on the calculation and the given options.

Step-by-Step Solution:
Radius r = 10 / 2 = 5 m. Height h = 3 m. Volume of tent V = (1/3) * pi * r^2 * h. V = (1/3) * pi * 5^2 * 3 = (1/3) * pi * 25 * 3. The factor 3 cancels with 1/3, so V = 25 * pi cubic metres. Using pi ≈ 3.14, V ≈ 25 * 3.14 = 78.5 m^3 (approximately). Volume per person = 3.92 m^3. Number of persons ≈ 78.5 / 3.92 ≈ 20.02. Thus, approximately 20 persons can be seated inside the tent.

Verification / Alternative check:
We can perform a quick check by multiplying 20 * 3.92 = 78.4 m^3, which is extremely close to the total tent volume of about 78.5 m^3. If we try 21 persons, 21 * 3.92 ≈ 82.32 m^3, which exceeds the tent volume. This confirms that 20 is the most reasonable maximum number of persons that fit given the stated air requirement per person.

Why Other Options Are Wrong:
Options 17, 18 and 19 are all too small and would leave unused volume given the assumed space requirement. Option 22 would demand a total air volume of about 86.24 m^3, which the tent does not have. Therefore, those options do not match the physical constraint of the tent's volume compared to per-person requirement.

Common Pitfalls:
Students sometimes confuse diameter with radius and incorrectly use r = 10 m in the cone volume formula, which doubles the radius and quadruples the area, leading to huge errors in volume. Another pitfall is using an incorrect approximation for pi or miscalculating 25 * pi. Finally, some may incorrectly round the number of persons up rather than choosing the nearest feasible integer that does not exceed the tent volume.

Final Answer:
The tent can accommodate approximately 20 persons.