The area of a circle is calculated using the formula π r². Given the radius r = 6 cm and π = 22/7, the area of the circle is (22/7) × 6² = (22/7) × 36 = 792/7 square cm.

A circle of radius $6$ cm is inscribed in a Square. Find the area of the shaded region.

Answer: The area of the shaded region is $\frac{216}{7}$ cm $^2$ .

Step-by-step solution

Step 1: Determine the side length of the square

When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. Since the radius is given as $6$ cm, the diameter will be $2 \times 6 = 12$ cm. Therefore, the side length of the square is $12$ cm.

Step 2: Calculate the area of the square

The area of a square is calculated by squaring its side length. With a side length of $12$ cm, the area of the square is $12^2 = 144$ square cm.

Step 3: Calculate the area of the circle

The area of a circle is calculated using the formula $\pi r^2$ . Given the radius $r = 6$ cm and $\pi = 22/7$ , the area of the circle is $(22/7) \times 6^2 = (22/7) \times 36 = 792/7$ square cm.

Step 4: Calculate the area of the shaded region

The shaded region is the area of the square minus the area of the inscribed circle. Subtracting the area of the circle from the area of the square gives $144 - 792/7 = (1008 - 792)/7 = 216/7$ square cm.

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A circle of radius 666 cm is inscribed in a Square. Find the area of the shaded region.