The area of a circle is calculated using the formula π r². Given the radius r = 9 cm and π = (22)/(7), the area of the circle is (22)/(7) × (9 cm)² = (22)/(7) × 81 cm² = (1782)/(7) cm².

A circle of radius $9$ cm is inscribed in a square. Find the area of the shaded region. Use $\pi = \frac{22}{7}$ .

Answer: The area of the shaded region is $\frac{486}{7} \text{ cm}^2$ .

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 of the circle is given as $9 \text{ cm}$ , the diameter will be $2 \times 9 \text{ cm} = 18 \text{ cm}$ . Therefore, the side length of the square is $18 \text{ cm}$ .

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 $18 \text{ cm}$ , the area of the square is $18^2 = 324 \text{ cm}^2$ .

Step 3: Calculate the area of the circle

The area of a circle is calculated using the formula $\pi r^2$ . Given the radius $r = 9 \text{ cm}$ and $\pi = \frac{22}{7}$ , the area of the circle is $\frac{22}{7} \times (9 \text{ cm})^2 = \frac{22}{7} \times 81 \text{ cm}^2 = \frac{1782}{7} \text{ cm}^2$ .

Step 4: Calculate the area of the shaded region

The shaded region represents the area of the square that is not covered by the circle. To find this area, we subtract the area of the circle from the area of the square. So, $324 \text{ cm}^2 - \frac{1782}{7} \text{ cm}^2 = \frac{324 \times 7 - 1782}{7} \text{ cm}^2 = \frac{2268 - 1782}{7} \text{ cm}^2 = \frac{486}{7} \text{ cm}^2$ .

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A circle of radius 999 cm is inscribed in a square. Find the area of the shaded region. Use π=227\pi = \frac{22}{7}π=722​.