Question

Find the area of a circle with maximum area that can be inscribed in a square of side 7 cm.

Hint:

The area of an inscribed circle is calculated using the formula \( A = \pi r^2 \), where \( r \) is half the side length of the square.

Answer 1

Step 1: Understand the geometry of the problem.
The maximum area of a circle inscribed in a square occurs when the circle touches all four sides of the square. The diameter of the circle is equal to the side length of the square.
Step 2: Calculate the radius of the circle.
Given that the side of the square is 7 cm, the diameter of the circle is also 7 cm. Therefore, the radius \( r \) of the circle is: \[ r = \frac{7}{2} = 3.5 \, \text{cm} \]
Step 3: Find the area of the circle.
The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] Substitute \( r = 3.5 \, \text{cm} \): \[ A = \pi (3.5)^2 = \pi \times 12.25 \approx 38.48 \, \text{cm}^2 \]