Question

A square of side 7 cm encloses a circle touching all its four sides. Then the area enclosed between the square and the circle is

• A. \(21 \text{ cm}^2\)
• B. \(15 \text{ cm}^2\)
• C. \((7-\pi)\ \text{cm}^2\)
• D. \(10.5 \text{ cm}^2\)

Answer 1

The Correct Option is D

The area enclosed between the square and the circle can be found by subtracting the area of the circle from the area of the square.
1. The side length of the square is 7 cm. Therefore, the area of the square is: \[ \text{Area of square} = \text{side}^2 = 7^2 = 49 \, \text{cm}^2 \] 2. The circle is inscribed in the square, so its diameter is equal to the side of the square, i.e., 7 cm. The radius of the circle is half of the diameter: \[ \text{Radius of the circle} = \dfrac{7}{2} = 3.5 \, \text{cm} \] 3. The area of the circle is given by the formula: \[ \text{Area of circle} = \pi r^2 = \pi (3.5)^2 = 12.25 \pi \, \text{cm}^2 \] 4. The area enclosed between the square and the circle is the difference between the area of the square and the area of the circle: \[ \text{Enclosed area} = 49 - 12.25 \pi \] Approximating \(\pi \approx 3.14\): \[ \text{Enclosed area} \approx 49 - 12.25 \times 3.14 = 49 - 38.415 = 10.585 \, \text{cm}^2 \]

The correct option is (D): \(10.5 \text{ cm}^2\)