The area of a circle is $\displaystyle 220 \text{cm}^{2}$. The side of the square inscribed in this circle will be ?
- $\sqrt{140} \text{cm}$
- $\sqrt{210} \text{cm}$
- $\sqrt{70} \text{cm}$
- $\sqrt{35} \text{cm}$
Area of circle = pi * r^2 = 220. r^2 = 220/pi. For a square inscribed in a circle, the diagonal of the square is the diameter of the circle. d = 2r. Diagonal = s * sqrt(2) = 2r. s^2 * 2 = 4r^2. s^2 = 2r^2 = 2 * (220/pi) = 440/pi. Using pi = 22/7, s^2 = 440 / (22/7) = 140. So s = sqrt(140).
Let the radius of the circle be r, so its area is given by the formula pi times r squared, which equals 220. This gives r squared equal to 220 divided by pi, or 220 divided by 3.14, resulting in approximately 70. The diagonal of an inscribed square equals the diameter of the circle, which is 2r, and the area of a square using its diagonal is half the diagonal squared, giving an area of half of 4r squared, which is 2r squared. Multiplying the value of r squared by 2 gives an area of 140 square centimeters, making the side of the square equal to the square root of 140 centimeters.