Two equal circle are drawn in square in such a way that a side of the square forms diameter of each circle. If the remaining area of the square is 42 cm2, how much will the diameter of the circle measure ?

Answer: Option C

Solution

Answer: Option C

Solution:

Let length of each side of square = 2π
According to the question,
$$\begin{array}{rl}& \frac{\pi r^2}{2}+\frac{\pi r^2}{2}+42=\text{Area of square}\\ & \Rightarrow \pi r^2+42=4r^2\\ & \Rightarrow 4r^2-\pi r^2=42\\ & \Rightarrow r^2\left(4-\frac{22}{7}\right)=42\\ & \Rightarrow r^2\left(\frac{28-22}{7}\right)=42\\ & \Rightarrow \frac{6r^2}{7}=42\\ & \Rightarrow r^2=\frac{42\times 7}{6}\\ & \Rightarrow r^2=7\times 7\\ & \Rightarrow r=7\\ & \therefore 2r=14cm\end{array}$$