Question

Two concentric circles have circumference 88cm and 198cm respectively calculate the ratio of their radii and the ratio of their area

Answer 1

Answer:

let the 1st circle have radius x cm and the 2nd circle have radius ycm

so,

2πx=88

x=88/2π=88×7/2×22=14

again ,

2πy=198

y=198/2π=198×7/2×22=63/2

ratio of their radii is 14:63/2

= 28:63=4:9

ratio of their area

π(14)^2:π(63/2)^2

=(14)^2:(63/2)^2

=14×14:63/2×63/2

=2×2:9/2×9/2

=4:81/4

=16:81

Answer 2

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

Circles are concentric circles

Circumference of larger circle = 198cm

Circumference of inner circle = 88cm

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

Ratio of radius = ??

Ratio of area = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{Circumference = 2\pi R}}}}$

Let the radius of outer circle be R

Let the radius of inner circle be r

: $\sf\implies\:{\bold{ \dfrac{ 2\pi R}{ 2\pi r } = \dfrac{198}{88} }}$

⠀⠀⠀⠀

: $\sf\implies\:{\bold{ \dfrac{R}{r} = \dfrac{99}{44} }}$

⠀⠀⠀⠀

: $\sf\implies \: {\bold{ \dfrac{R}{r} = \dfrac{9}{4} }}$

⠀⠀

$\sf{\pink{\boxed{\bold{Ratio\: of \: radius = 9 : 4 }}}}$

⠀⠀⠀⠀

$\sf{\red{\boxed{\bold{Area = \pi r^2}}}}$

⠀⠀

: $\sf\implies\: {\bold{\dfrac{\pi R^2}{\pi r^2}}}$

⠀⠀⠀⠀

: $\sf\implies\:{\bold{\dfrac{ R^2}{r^2} }}$

⠀⠀⠀⠀

: $\sf\implies\:{\bold{ \dfrac{9^2}{4^2} }}$

⠀⠀⠀⠀

: $\sf\implies\:{\bold{ \dfrac{81}{16} }}$

⠀⠀⠀⠀

$\sf{\pink{\boxed{\bold{Ratio\: of\: area =\dfrac{81}{16}}}}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

Ratio of circumference = 9:4

Ratio of area = 81 : 16