Question

Find the area of the largest circle that can be inscribed in a rectangle of \(18\, \text{cm} \times 14\, \text{cm}\).

• A. 49 cm\(^2\)
• B. 154 cm\(^2\)
• C. 378 cm\(^2\)
• D. 1078 cm\(^2\)

Hint:

Largest inscribed circle in a rectangle touches the shorter side completely.

Answer 1

The Correct Option is B

The largest circle inscribed in a rectangle will have a diameter equal to the smaller side of the rectangle.
Here, the rectangle has sides 18 cm and 14 cm, so diameter \(d = 14\, \text{cm}\).
Radius \(r = \frac{d}{2} = \frac{14}{2} = 7\, \text{cm}\).
Area of circle \(= \pi r^2 = \pi \times 7^2 = 49\pi \approx 49 \times 3.14 = 153.86\, \text{cm}^2\).
Hence, the area of the largest inscribed circle is approximately \(\boxed{154\, \text{cm}^2}\).