Question

Find the radius and circumference of a circle, whose area is:
(i) 1386 cm^2
(ii) 3850 cm^2
please answer with prosedure properly​

Answer 1

$\star\boxed{\mathfrak\pink{\underline{\underline{Answer}}}}\star$

$\textbf{i)\:\:3\:cm\:and\:18.8571428571\:cm}$

$\textbf{ii)\:\:35\:cm\:220\:cm}$

$\star\star\boxed{\mathbb\red{\underline{\underline{GIVEN}}}}\star\star$

$\odot\textbf{Area\:of\:first\:circle\:=\: 1386\:{cm}^2 }$

$\odot\textbf{Area\:of\:second\:circle\:=\: 3850\:{cm}^2 }$

$\star\star\star\boxed{\mathbb\green{\underline{\underline{TO\: CALCULATE}}}}\star\star\star$

$\odot\textbf{Radius\:and\: circumference\:of\:both\:circles}$

$\star\star\star\star\boxed{\mathcal\red{\underline{\underline{Explanation}}}}\star\star\star\star$

$\textbf{Let\:the\:radius\:of\:first\:and\:second\:circle\:be\:r\:and\:R.}$

$\boxed{\textsf{Area of circle = \pi\:r^2 }}$

$\mathbb{I}$

$\Longrightarrow\textsf{ 1386\:cm^2=\pi\:r^2 }$

$\textsf{Substituting the value of \pi\:as\:\dfrac{22}{7} }$

$\Longrightarrow\textsf{ 1386\:{cm}^2=\:\dfrac{22}{7}\:\times\:r^2 }$

$\textsf{ \dfrac{1386\:\times\:7}{22} =r^2 }$

$\Longrightarrow\textsf{ r^2=9\:{cm}^2 }$

$\huge\boxed{\textbf{r=3\:cm}}$

$\Longrightarrow\textsf{ 1386\:cm^2=\pi\:r^2 }$

$\textsf{Substituting the value of \pi\:as\:\dfrac{22}{7} }$

$\Longrightarrow\textsf{ 3850\:{cm}^2=\:\dfrac{22}{7}\:\times\:R^2 }$

$\textsf{ \dfrac{3850\:\times\:7}{22} =R^2 }$

$\Longrightarrow\textsf{ R^2=1225\:{cm}^2 }$

$\huge\boxed{\textbf{R=35\:cm}}$

$\huge\boxed{\textsf{Circumference}}$

$\boxed{\textsf{Circumference of Circle= 2\pi\:\times\:r }}$

$\textsf{where r is the radius of the circle }$

$\textsf{Circle 1 = 2\times\:\pi\:3\:cm }$

$\boxed{\textsf{Circumference of Circle 1=18.8571428571 cm}}$

$\textsf{Circle 2= 2\times\:\pi\:35\:cm }$

$\boxed{\textsf{Circumference of Circle 2 = 220 cm}}$

$\therefore\textbf{The\:Answer\:is}$

$\textbf{i)\:\:3\:cm\:and\:18.8571428571\:cm}$

$\textbf{ii)\:\:35\:cm\:and\:220\:cm}$

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