A conical tent is 15 m high, and the radius of its base is 8 m. Find the cost of the canvas required to make the tent at the rate of ₹21 per m². [Use π = 22/7]

Appeared in: Bihar NHM CHO-2025

Explanation

The problem requires calculating the cost of canvas for a conical tent, which means finding the Curved Surface Area (CSA).
First, the slant height (l) is calculated using the Pythagorean theorem: l = √(r² + h²) = √(8² + 15²) = √289 = 17 m.
Next, the CSA is calculated using the formula CSA = πrl: CSA = (22/7) × 8 × 17 = 2992/7 m².
Finally, the total cost is found by multiplying the CSA by the rate: Cost = (2992/7) × 21 = 2992 × 3 = ₹8,976.

Option A: This value is incorrect and likely results from a miscalculation during the multiplication of the area and the cost.
Option C: This value is incorrect. It may arise from an error in calculating the slant height or the curved surface area.
Option D: This incorrect value is obtained if the height (h = 15 m) is used instead of the slant height (l = 17 m) when calculating the curved surface area. (Area = πrh = (22/7)×8×15 = 2640/7; Cost = (2640/7)×21 = 7920).

Visual 1: Diagram - A diagram of a cone illustrating the relationship between the vertical height (h), the radius (r), and the slant height (l) as the sides of a right-angled triangle. This helps visualize why the Pythagorean theorem is used.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Mensuration - Surface Area and Cost Calculation for a Cone as background academic context rather than a clinical decision trigger.
This question tests quantitative aptitude and basic geometry, a non-nursing subject area that is part of the nursing examination syllabus.
Strong analytical and calculation skills are essential for various nursing tasks, such as medication dosage calculations, fluid balance monitoring (I/O charting), and interpreting numerical data from medical reports.
What if the question asked for the total area of the ground covered by the tent? In that case, you would calculate the area of the circular base using the formula A = πr², which would be (22/7) × 8² ≈ 201.14 m².

How to Approach the Question

First, identify the geometric shape in the question (a conical tent) and what needs to be calculated (cost of canvas).
Recognize that the 'canvas' corresponds to the Curved Surface Area (CSA) of the cone, not the total surface area (which would include the base).
List the given parameters: height (h = 15 m) and radius (r = 8 m).
Recall the formula for the slant height (l) of a cone, l = √(r² + h²), and calculate it.
Use the calculated slant height in the formula for the CSA of a cone: CSA = πrl.
Finally, multiply the calculated CSA by the given cost per unit area (₹21 per m²) to find the total cost.

Concept Tested & Keywords

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Practise the full Bihar NHM CHO-2025

Attempt every question from this paper in a timed mock, then review the full solution for each one.