Question

The area of a circle is increased by 22 cm² when its radius is increased by 1 cm.
The original radius of the circle is

(a) 6 cm (b) 3 cm (c) 4 cm (d) 3.5 cm

Answer 1

Let r be the radius of the circle. Then
Area of original circle = $\mathit{\text{π}}$r² cm²
Radius of circle after increment = (r + 1) cm
Thus,as per the question
$$\begin{gathered} \pi {\left(r+1\right)}^2\mathit{-}\pi r^2=22 \\ \Rightarrow {\left(r+1\right)}^2-r^2=\frac{22}{{\displaystyle \frac{22}{7}}}=7 \\ \Rightarrow r^2+2r+1-r^2=7 \\ \Rightarrow r=3\mathrm{cm} \end{gathered}$$
Thus, the original radius of the circle is 3 cm.
Hence, the correct option is (b).