The difference between the circumference and the diameter of a circle is 30 cms. The area of this circle is

Appeared in: RRB Staff Nurse Kolkata-2015

Explanation

The problem provides the relationship: Circumference - Diameter = 30 cm.
Using the formulas C = 2πr and d = 2r, the equation becomes 2πr - 2r = 30.
Factoring out 2r gives 2r(π - 1) = 30. Substituting π = 22/7, we get 2r(15/7) = 30.
Solving for the radius (r) yields r = 7 cm.
The area of the circle is calculated using the formula A = πr², which is (22/7) * 7² = 154 cm².

Option B: This area corresponds to a radius of 14 cm. A student might arrive at this if they incorrectly double the calculated radius before finding the area.
Option C: This value is exactly double the correct area. This suggests a simple calculation error, such as multiplying by 2 unnecessarily at the final step.
Option D: This value is three times the correct area. This is likely a significant miscalculation or a guess.

Visual 1: Diagram - An annotated diagram of a circle showing the radius (r), diameter (d=2r), and the circumference, illustrating the relationship between these components.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the area of a circle from a given relationship between its circumference and diameter as background academic context rather than a clinical decision trigger.
This question tests fundamental mathematical aptitude, which is a non-nursing component of the examination.
Strong numeracy skills are essential for nurses for tasks like medication dosage calculation, interpreting lab results, and monitoring patient vitals.
What if the question stated the sum of the circumference and diameter was 88 cm? The equation would be 2πr + 2r = 88. Solving this gives 2r(π + 1) = 88, which leads to 2r(29/7) = 88, so r = (88 * 7) / (2 * 29) ≈ 10.6 cm. The area would then be π * (10.6)².

How to Approach the Question

First, identify the key information given: 'the difference between the circumference and the diameter of a circle is 30 cms'.
Translate this word problem into a mathematical equation. Let 'C' be circumference and 'd' be diameter. The equation is C - d = 30.
Express C and d in terms of the radius 'r'. C = 2πr and d = 2r.
Substitute these into the equation: 2πr - 2r = 30.
Solve this equation for 'r'. Use the approximation π = 22/7.
Once you have the value for the radius 'r', use the formula for the area of a circle, A = πr², to find the final answer.

Concept Tested & Keywords

Concept Tested: Calculating the area of a circle from a given relationship between its circumference and diameter.
Stem keywords: circumference, diameter, circle, area, difference
Lead-in keywords: The area of this circle is

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