Question

The ratio of the radii of two circle is 9:16 then find the ratio of their circumference

Answer 1

As we know that

Circumference= 2πR

C is directly proportional to R

C~R

So the ratio of Radii of two circles will be same as the Circumference.

C1:C2= R1:R2

C1:C2= 9:16

Answer 2

$\huge\rm\underline\purple{Question :-}$

The ratio of the radii of two circle is 9:16. Find the ratio of their circumferences.

$\huge\rm\underline\purple{Answer :-}$

$\green{\underline\bold{Given,}}$

• Ratio of the radii of two circle is 9:16

$\sf Now\begin{cases} &\sf{Let\;the\;radius\; of \;the\;first\;circle \;be\; =\be{r1}}\\&\sf{Let\;the\;radius\;of\;the\;second\;circle\;be =\bf{r2}}\end{cases}$

$\blue{\underline\bold{We\:know,}}$

$\boxed{ \sf \pink{ Circumference\: of\: the \: circle \: =\: 2Πr}}$

$\orange{\underline\bold{For\:the\:first\:circle,}}$

✏ C1 = 2Πr1

$\orange{\underline\bold{For\:the\:second\:circle,}}$

✏ C2 = 2Πr2

✯Therefore,

$\frac{C1}{C2}$=$\frac{2Πr1}{2Πr2}$

$\frac{r1}{r2}$=$\frac{9}{16}$

$\red{\underline\bold{ ∴ \:Ratio\:of\:their\:circumference}}$=$\frac{9}{16}$

= 9:16

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