Question

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Circumference of two circle are in ratio 5:4. Find the ratio of their area
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Spamming = 20 answers reported ​

Answer 1

Answer:

$The \: ratio \: of \: the \: circumference \: of \: the \: circle \: = \: 5:4$

$let \: the \: circumference \: of \: ratio \: = \: 5x \\\\\ \: 2\pi \: r = 5x \\ r = \frac{5x}{2\pi}$

= the circumference of second ratio : 4x

$2\pi \: r \: = \: 4x \\ r =\frac{4x}{2\pi}$

$Ratio \: between \: their \: radii \: = \frac{5x}{2\pi} \: : \: \frac{4x}{2\pi} \: = \: 5:4$

hope it's helped

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Answer 2

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Let r¹ and r² be the radii of two given circles and C¹ and C² be their circumference respectively

So ,

C¹ = 2 pie r¹

C² = 2 pie r²

Then

C¹/C² = 5/4

So,

2 pie r¹/ 2 pie r² = 5/4

Let A¹ and A² be the area of two

circles respectively

We have A¹ and A² be the

area of two circle respectively

A¹ = pie r¹ A² = pie r²

So, A¹/A² = pie r¹/ pie r²

(r¹/r²) = (5/4)²

= 25/16

$\huge{ \green{ \tt{ \underbrace{ \underline{hence \: verified}}}}}$

Ratio of given ratio

of circle = 25/16