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: Relate the side of the square to the circle.
For the largest circle that can fit inside a square, the diameter of the circle is equal to the side length of the square. Hence, \[ d = 7 \text{ cm} \]
Step 2: Use the diameter directly in the area formula.
The area of a circle can also be written as: \[ A=\frac{\pi d^2}{4} \] Substitute \(d=7\) cm: \[ A=\frac{\pi(7)^2}{4} =\frac{49\pi}{4} =12.25\pi \]
Step 3: Compute the final value.
Using \(\pi \approx 3.1416\), \[ A=12.25\times3.1416\approx38.48\ \text{cm}^2 \] Therefore, the maximum area of the inscribed circle is: \[ \boxed{38.48\ \text{cm}^2} \]