The area of a circle is increased by 22 sq. cm if its radius is increased by 1 cm. The original radius of the circle is :

Answer: Option A

Let the original radius of the circle be R cm
Then,
$$\begin{array}{rl}& \pi \left[{\left(R+1\right)}^2-R^2\right]=22\\ & \Rightarrow \left(2R+1\right)=\frac{22\times 7}{22}\\ & \Rightarrow 2R+1=7\\ & \Rightarrow 2R=6\\ & \Rightarrow R=3cm\end{array}$$