Question

8. Thecircumferences of two circles are in the ratio 1:3. Find the ratio of their areas.​

Answer 1

Answer:

Circumference=2πri:2πr 2 = 1:3

r1:r2=1:2

area

πr 1^2:πr 2^2 = πx1^2:πx3^2

= I:9

Ratio of areas of circles = 1:9

Answer 2

Step-by-step explanation:

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The circumferences of two circles are in the ratio 1:3. Find the ratio of their areas.

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$\\ \\ Ratio \: of \: their \: circumference \\ is \: given \: in \: ratio \: 1:3$

$let \: r1 \: be \: radius \: of \: smaller \: circle \\ r2 \: be \: radius \: of \: bigger \: circle$

$\implies \frac{(2\pi \: r1)}{2\pi \: r2} = \frac{1}{3} \\ \\ \implies \frac{( \cancel{2\pi} \: r1)}{ \cancel{2\pi} \: r2} = \frac{1}{3} \\ \\ \implies r2 = 3(r1)$

$\\ \\ So, \: the \: ratio \: of \: their \: areas \: will \: \\ be \: given \: by \implies \\ \\ { \implies \frac{area \: 1}{area \: 2} = \frac{ \cancel \pi \: {(r1)}^{2} }{ \cancel \pi \: {(3r1)}^{2} } } \\ \\ \implies { \frac{area \: 1}{area \: 2} = \frac{ \cancel{{(r1)}^{2} }}{9 { \cancel{(r1)}^{2} }} } \\ \\ \implies { \frac{area \: 1}{area \: 2} = \frac{1}{9} } \\ \\ \huge \boxed{{So, \: the \: ratio \: of \: their \: areas \: is \: 1:9 }}$