Question

The area of a circle is increased by $22{cm}^2$ when its radius is increased by $1cm$. The original radius of the circle is:

• A. $3cm$
• B. $5cm$
• C. $7cm$
• D. $9cm$

Answer 1

The correct option is A $3cm$

Let the radius be 'r'

Radius increased by 1 cm so,

New radius be 'r+1'

So, as per question

$\Rightarrow \pi (r+1{)}^2-\pi r^2=22$

$\Rightarrow \pi \left[\right(r+1{)}^2-r^2]=22$

$\Rightarrow \frac{22}{7}[r^2+2r+1-r^2]=22$

$\Rightarrow 2r+1=7$

$\Rightarrow 2r=6$

$\Rightarrow r=3cm$