Canvas needed for a tent (cylinder + cone, r = 10 m)\nA tent is formed by a cylinder of radius 10 m and height 5 m, surmounted by a cone of the same radius with slant height 15 m. How much canvas is required if 20% extra is allowed for folding/stitching? (Use π = 22/7. Ignore floor.)

Difficulty: Medium

Correct Answer: None of these

Explanation:


Introduction / Context:
Canvas required equals the lateral areas (outer surface only) since tents typically exclude the base/floor unless specified. Here a cylinder is topped by a cone. We compute each lateral area and then add 20% wastage for folds and stitching.


Given Data / Assumptions:

  • Cylinder: radius r = 10 m, height h = 5 m
  • Cone: same radius r = 10 m, slant height l = 15 m
  • π = 22/7; base is not included (canvas excludes floor).
  • Extra allowance = 20% of computed lateral area.


Concept / Approach:
Lateral area (cylinder) = 2 * π * r * h. Lateral area (cone) = π * r * l. Sum, then multiply by 1.20 to account for extra canvas.


Step-by-Step Solution:

A_cyl = 2 * π * r * h = 2 * (22/7) * 10 * 5 = 100 * (22/7) = 2200/7 ≈ 314.286 m^2 A_cone = π * r * l = (22/7) * 10 * 15 = 150 * (22/7) = 3300/7 ≈ 471.429 m^2 A_total = 2200/7 + 3300/7 = 5500/7 ≈ 785.714 m^2 Canvas (with 20% extra) = 1.2 * 5500/7 = 6600/7 ≈ 942.857 m^2


Verification / Alternative check:
If a floor were included, add πr^2 = (22/7) * 100 = 2200/7 ≈ 314.286, yielding ≈ 1320 m^2 even then. None of the given options match ≈ 943 m^2 or ≈ 1320 m^2.


Why Other Options Are Wrong:
All numeric choices are far larger than either interpretation (with or without base). Hence the correct selection within this set is “None of these.”


Common Pitfalls:
Including the base by default or using circumference * slant height for the cone incorrectly. Maintain unit consistency and apply the 20% only after summing areas.


Final Answer:
None of these

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