Question

31. The area of a circle is increased by 22 cm when its radius is increased by 1 on. The
orignal radius of the circle is
(a) 6 cm
(b) 3.2 cm
(c) 3 cm
d) 3.5 cm​

Answer 1

Answer:

C

Step-by-step explanation:

Let original radius be r.

Then, according to the question,

π(r+1)2−πr2=22

=> π×[(r+1)2−r2]=22

=>

22

7

×(r+1+r)(r+1−r)=22

=> 2r+1=7 => 2r=6

r=

6

2

=3 cm

Answer 2

Answer

$\textbf{3 cm}$

Here is the attachment

By the way , I am terribly sorry for that horrible handwriting

$\underline{\bf{Explanation\::}}$

Now the hardest step is the part where we subtract

$\pi {(r + 1)}^{2}$ and $\: \pi {r}^{2}$

Now , in the question it is given that with one centimetre increase the radius, there is 22cm² increase in the area.

Going with this information, we can see that the final area minus the initial area is 22 centimetres²

now the final area is

$\sf \pi {(r + 1)}^{2}$

And the initial area is

$\sf \pi {r}^{2}$

Hope you had a nice day