The length and width of a rectangle are 14 meters and 7 meters respectively. Find the area of the maximum circle?

Appeared in: Maharashtra CHO - 2020

Explanation

The core concept is that the largest circle that can be inscribed within a rectangle will have a diameter equal to the shorter of the rectangle's two sides.
Given the rectangle's dimensions are 14 m and 7 m, the shorter side is 7 m. This becomes the diameter of the maximum circle.
The radius is half the diameter, so the radius (r) is 7 m / 2 = 3.5 m.
Using the area formula for a circle, Area = πr², the calculation is (22/7) × (3.5)² = 38.5 square meters.

Option A: This answer (154 sq m) results from incorrectly using the shorter side (7 m) as the radius instead of the diameter.
Option B: This value (16.25 sq m) does not correspond to a logical calculation based on the given dimensions and standard geometric formulas. It is an incorrect calculation.
Option D: This answer (616 sq m) results from incorrectly using the longer side (14 m) as the radius. A circle with a 14 m radius (28 m diameter) would not fit inside the 14 m × 7 m rectangle.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Area of a Circle within a Rectangle as background academic context rather than a clinical decision trigger.
This question tests basic mathematical aptitude and logical reasoning, skills that are essential for problem-solving in various fields, including nursing.
Accurate calculation is a fundamental skill for nurses, especially for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data.
What if the question asked for the area of the largest square inside the rectangle? The side of the largest square would also be limited by the shorter side of the rectangle (7m), and its area would be 7m × 7m = 49 sq m.

How to Approach the Question

First, identify the given information: the shape is a rectangle with a length of 14 m and a width of 7 m.
Recognize the key constraint: the question asks for the area of the 'maximum circle' that can fit inside.
Deduce that the diameter of this circle must be equal to the shorter side of the rectangle to maximize its area while still fitting within the boundaries.
Set the diameter of the circle to 7 m.
Calculate the radius by dividing the diameter by 2 (radius = 3.5 m).
Apply the formula for the area of a circle, A = πr², using the calculated radius.

Concept Tested & Keywords

QWQQ4kd1O2QIbiqmV8efa0

Practise the full Maharashtra CHO - 2020

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