Question

(3) The ratio of the radii of two circles is 2:3. Find the ratio of their areas.
f the area of the bigger circle is 3123 sq. cm, find the area of the
smaller circle.​

Answer 1

Let:-

Let radius of small circle be r

Let radius of bigger circle be R

Given:-

Ratio of radius of two circles is 2:3

So we also write it as

$\mathtt{ \frac{r}{R} = \frac{2}{3} }$

Now square both sides and multiply with π on both sides.

$\mathtt{ \frac{\pi(r)^{2} }{(R) ^{2}} = \frac{ {2}^{2}\pi }{ {3}^{2} } }$

$\mathtt{ \frac{ {r}^{2} }{ {R}^{2} } = \frac{4}{9} }$

$\mathtt{ {r}^{2} = \frac{4}{9} R^{2} }$

$\mathtt{Area \: of \: big \: circle = 3123 {cm}^{2} }$

$\mathtt{ {\pi \: R}^{2} = {3123cm}^{2} }$

$\mathtt{R^{2} = \frac{3123}{\pi} }$

$\mathtt{Area \: of \: small \: circle \: is \: π {r}^{2} }$

$\mathtt{ π = \frac{4}{9} r}$

$\mathtt{ π {r}^{2} = \pi \times \frac{4}{9} {R}^{2} }$

$\mathtt{ \pi {r}^{2} = \pi \times \frac{4}{9} \times \frac{3123}{\pi} }$

$\mathtt{ = 1388 {cm}^{2} }$

Hope this helps you.

# By Sparkly Princess