Question

The ratio of the radii of two circles is 8: 15. Find the ratio of their circumferences.​

Answer 1

$\bold {Given}\begin{cases} \sf \: The \: ratio \: of \: \: the \: radii \: of \: two \: circles \: is \: \bold{8:15} \end{cases}$

$\sf\underline{We \: have \: to \: find \: the \: ratio \: of \: their \: circumferences}.$

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$\sf\underline{As \: we \: know \: that} :$

$\bigstar\boxed{\boxed{\bold\purple{circumference \: of \: a \: circle \: = \: 2\pi \: r}}}$

☯︎ Let

• $\sf \: \bold{r1} \: be \: the \: radius \: of \: first \: circle \:$

• $\bold{r2} \sf \: be \: the \: radius \: of \: second \: circle$

• $\bold{c1} \sf \: be \: the \: circumference \: of \: first \: circle$

• $\bold{c2} \sf \: be \: the \: circumference \: of \: second \: circle$

Now,

$\sf:\implies \: \dfrac{c1}{c2} = \dfrac{2\pi \: r1}{2\pi \: r2}$

$\sf:\implies \: \dfrac{c1}{c2} = \dfrac{2\pi8x}{2\pi15x}$

$\sf:\implies \: \dfrac{c1}{c2} =\cancel \dfrac{2\pi8x}{2\pi15x}$

$\sf:\implies \: \dfrac{c1}{c2} = \boxed{\boxed{\bold\purple{ \frac{8}{15} }}}\bigstar$

$\sf\therefore{\underline{Hence, \: the \: ratio \: of \: their \: circumferences \: is \: \bold{ \dfrac{8}{15}} }}$

Answer 2

Answer:

$\mathfrak{ \large{\blue{ \underline{ \purple{ Given: }}}}}\mathfrak{ \large{\blue{ \underline{ \purple{ Given: }}}}}Given:</p><p></p><p>Radius of circle = 20 cm</p><p></p><p>Value of π = 3.14</p><p></p><p>\mathfrak{ \large{\blue{ \underline{ \purple{ To \: Find: }}}}}</p><p></p><p>Area and perimeter of circle</p><p></p><p>\mathfrak{ \large{\blue{ \underline{ \purple{ Solution:}}}}}</p><p>\:\:\:\:\:\:\:\:\:\:\:\:\: \mathfrak{ \underline{ \green{Formula \: to \: calculate \: the \: circumference \: of \: circle}}}Formulatocalculatethecircumferenceofcircle</p><p>\boxed{ \mathfrak{ \star \: \: \: { \red{ \large{circumference = 2 \times \pi \times radius}}}}}⋆circumference=2×π×radius</p><p></p><p>According to question,</p><p></p><p>\large{ \rm \longmapsto \: \: \: \: \: \: \: circumference = 2 \times 3.14 \times 20}⟼circumference=2×3.14×20</p><p>\large{ \rm \longmapsto \: \: \: \: \: \: \: circumference = \boxed{ \orange{ \mathfrak 125.6 \: cm}}}⟼circumference=125.6cm</p><p>\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \mathfrak{ \underline{ \green{Formula \: to \: calculate \: the \: circumference \: of \: circle}}}Formulatocalculatethecircumferenceofcircle</p><p>\boxed{ \mathfrak{ \star \: \: \: \: \: \: { \red{ \large{area = \pi \times {radius}^{2} }}}}}⋆area=π×radius2</p><p></p><p>According to question,</p><p></p><p>\large{ \rm \longmapsto \: \: \: \: \: \: \: area = 3.14 \times {20}^{2}}⟼area=3.14×202</p><p>\large{ \rm \longmapsto \: \: \: \: \: \: \: area = 3.14 \times 20 \times 20}⟼area=3.14×20×20</p><p>\large{ \rm \longmapsto \: \: \: \: \: \: \: area = \boxed{ \orange{ \mathfrak{1256 \: {cm}^{2} }}}}⟼area=1256cm2 \\ \\ \mathfrak{ \large{\blue{ \underline{ \purple{ Hence:}}}}}Hence:</p><p>The area and circumference of circle is 125.6 cm and 1256 cm²</p><p>$