Question

The ratio of radii of two circles are in the ratio of 1:2 what will the ratio of the area

Answer 1

GIVEN :-

Radii of two circles are in ratio 1:2

TO FIND :- Ratios of their areas

FORMULA :-

$ar.(circle) = \pi {r}^{2}$

SOLUTION :-

Let radius of smaller circle be 'r'

Radius of larger circle will be ' 2r '

Ratio of areas of two circle

= Area of circle 01 / Area of circle 02

$\frac{ \pi {r}^{2} }{\pi {(2r)}^{2} } \\ \\ \\ = \frac{\pi {r}^{2} }{\pi4 {r}^{2} } \\ \\ \\ = \boxed{ \frac{1}{4} }$

Therefore, ratio of their areas is 1:4

ADDITIONAL INFORMATION

In case of perimeters of circles,

Ratio of radius = Ratio of perimeter

In case of areas of circles,

(Ratio of radius)^ 2 = Ratio of Area

Answer 2

$\large{ \fbox{ \fbox{ \bold{Given :- \: }}}}$

$\to \: \: \: \bold{Radii \: Of \: Two \: Circles \: Are \: In \: Ratio \: 1 : 2 \: }$

$\large{ \fbox{ \fbox{ \bold{To \: Find :- \: }}}}$

$\to \: \: \bold{ \frac{ \: \: \: Area \: Of \: Smaller \: Circle \: \: }{ \: \: \: Area \: Of \: Larger \: Circle \: \: } = \: \: ? }</p><p>$

$\large{\fbox{ \fbox{ \bold{Solution :- \: }}}}$

$\large{ \bold{ \underline{ \: Let \: , \: \: }}}$

$\to \bold{Radius \: Of \: Smaller \: Circle = r \: \: } \\ \to \bold{Radius \: Of \: Larger \: Circle = 2r \: }$

$\large{ \bold{ \underline{We \: Know \: That \: ,</p><p> \: \: \: }}}$

$\huge{ \fbox{ \fbox{ \bold{Area \: Of \: Circle \: \: = \pi {r}^{2} }}}}$

$\large{ \bold{ \underline{So \: , \: \: }}}$

$\implies \: \bold{ \frac{ \: \: \: Area \: Of \: Smaller \: Circle \: \: }{ \: \: \: Area \: Of \: Larger \: Circle \: \: }} \\ \\ \implies \: \: \frac{\pi {(r)}^{2} }{\pi {(2r)}^{2} } \\ \\ \implies \: \: \frac{\pi {r}^{2} }{\pi4 {r}^{2} } \\ \\ \implies \: \: \frac{1}{4}$

$\bold{ \underline{Hence \: , \: \: Ratio \: Of \: Their \: Areas \: Is \: 1 : 4 \: }}$