Question

If the radius of the circle is increased to twice its original length.how much will the area of the circle is increase

Answer 1

Let original radius be r
hence original area

(a1)=
$a1 = \pi \: {r}^{2}$


Now radius is made 2 times


Hence new radius is 2r
now area (a2)


$a2 = \pi \: {(2r)}^{2} \\ a2 = 4\pi {r}^{2}$
hence
$\frac{a2}{a1} = \frac{4\pi {r}^{2} }{\pi {r}^{2} } \\ = 4$


Hence area will become four times

Answer 2

Let the radius of circle C(o,r) be x cm.
Then area is 22/7 x*2
Now let the radius be 2x cm,
Then area=22/7×2x*2
Hence,increment in area=22/7x*2÷22/7×(2x)*2
=1/4
Therefore the area will also increase four times