A path of 7 meters width runs around outside a circular park whose diameter is 90 m. The cost of leveling the path at Rs. 10.80 per m² is (nearest to a rupee):

1. A

   Rs. 22,834

2. B

   23,047

3. C

   22,810

4. D

   23,045

Appeared in: JSSH Staff Nurse - 2019

Explanation

• The first step is to determine the inner and outer radii. The inner radius (r) of the park is half its diameter (90 m / 2 = 45 m).
• The outer radius (R) is the inner radius plus the width of the path (45 m + 7 m = 52 m).
• The area of the path (an annulus) is calculated using the formula: Area = π(R² - r²). Using the value π = 22/7, the area is (22/7) * (52² - 45²) = (22/7) * (52-45) * (52+45) = (22/7) * 7 * 97 = 2134 m².
• The total cost is the area of the path multiplied by the cost per square meter: 2134 m² * Rs. 10.80/m² = Rs. 23,047.20.
• Rounding to the nearest rupee gives Rs. 23,047.

Why Other Options Were Wrong

• Option A: This value is incorrect and likely results from a miscalculation, such as an error in squaring the radii or during the final multiplication.
• Option C: This option is also a result of a calculation error. It is significantly lower than the correct cost.
• Option D: This value is very close to the correct answer but is incorrect. It may be the result of a minor rounding error at an intermediate step or a small mistake in the final multiplication.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Area of a circular path (annulus) and its application in cost calculation as background academic context rather than a clinical decision trigger.
• This question tests basic mathematical and aptitude skills, which are a component of many nursing entrance examinations.
• While not a direct clinical skill, the ability to perform accurate calculations is crucial in nursing for tasks like medication dosage calculation, IV drip rate monitoring, and fluid balance charting.
• What if the path was inside the park's boundary? In that case, the park's radius (45 m) would be the outer radius (R), and the inner radius (r) would be 45 m - 7 m = 38 m. The area and cost would be different.

How to Approach the Question

• First, carefully read the question to identify all the given information: the shape (circular park with a path), the dimensions (diameter of the park, width of the path), and the rate (cost per m²).
• Note the specific instruction provided in the image: Use π = 22/7.
• Calculate the radius of the inner circle (the park) from its diameter (r = D/2).
• Calculate the radius of the outer circle by adding the path's width to the inner radius (R = r + width).
• Use the formula for the area of an annulus (the path): Area = π(R² - r²). To simplify, use the algebraic identity: Area = π(R - r)(R + r).
• Substitute the values and calculate the area.

Concept Tested & Keywords

• Concept Tested: Area of a circular path (annulus) and its application in cost calculation.
• Stem keywords: path, circular park, diameter, width, cost of leveling
• Lead-in keywords: cost, nearest to a rupee

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