Question

The ratio of the radii of two circles is 1:10. Find the ratio of their areas.
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Answer 1

Answer:

Radii of two circles are in ratio 1:2

TO FIND :- Ratios of their areas

FORMULA :-

ar.(circle) = \pi {r}^{2}ar.(circle)=πr2

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

\begin{gathered}\frac{ \pi {r}^{2} }{\pi {(2r)}^{2} } \\ \\ \\ = \frac{\pi {r}^{2} }{\pi4 {r}^{2} } \\ \\ \\ = \boxed{ \frac{1}{4} }\end{gathered}π(2r)2πr2=π4r2πr2=41

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