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) 3.2 cm
(c) 3 cm
(d) 3.5 cm

Answer 1

(c) 3 cm

Suppose the radius of the original circle is r cm.
Area of the original circle = ${\mathrm{\pi r}}^2$

Radius of the circle = (r +1) cm
According to the question:
$\mathrm{\pi }{\left(\mathrm{r}+1\right)}^2={\mathrm{\pi r}}^2+22$
⇒ $\mathrm{\pi }\left({\mathrm{r}}^2+1+2\mathrm{r}\right)={\mathrm{\pi r}}^2+22$
⇒ ${\mathrm{\pi r}}^2+\mathrm{\pi }+2\mathrm{\pi r}={\mathrm{\pi r}}^2+22$
⇒ $\mathrm{\pi }+2\mathrm{\pi r}=22$ [cancel ${\mathrm{\pi r}}^2$ from both the sides of the equation]
⇒ $\mathrm{\pi }\left(1+2\mathrm{r}\right)=22$
⇒ $\left(1+2r\right)=\frac{22}{\mathrm{\pi }}=\left(\frac{22\times 7}{22}\right)=7$
⇒ 2r = 7 -1 = 6
∴ r = $\left(\frac{6}{2}\right)$ cm = 3 cm
∴ Original radius of the circle = 3 cm