Question

Find the area of circle if its circumference is 154 cm.
Pls explain with steps.

Answer 1

$\LARGE\mathfrak{\underline{\underline{✪\: \: \: Given :-}}}$

$\large\texttt{↦ Circumference of the circle = 154 cm .}$

$\LARGE\mathfrak{\underline{\underline{✪\: \: \: To \: \: find :-}}}$

$\large\texttt{↦ Area of the circle = ?}$

$\LARGE\mathfrak{\underline{\underline{✪\: \: \: Formula :-}}}$

$\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{red}{ Circumference_{ ( \: Circle \: ) } = 2 \pi r }}}\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{red}{ Area_ { ( \: Circle \: ) } = \pi r^{2} }}}$

$\LARGE\mathfrak{\underline{\underline{✪\: \: \: How \: \: to \: \: solve :-}}}$

• We have to calculate the radius of the circle with the help of the given circumference .

• The once the radius is calculated then we can find the Area of the circle .

$\LARGE\textbf{\underline{\underline{✪\: \: \: Solution :-}}}$

$\large\: \bigstar\textsf\textcolor{orange}{\: \: \: Circumference_{ ( \: Circle \: ) } = 2 \pi r }\\\\\\\large: \: \Longrightarrow\textsf{ 154 = 2 × \cfrac{22}{7} × r }\\\\\\\large: \: \Longrightarrow\textsf{ \cfrac{154 × 7 }{2 × 22} = r }\\\\\\\large: \: \Longrightarrow\textsf{ \cancel\cfrac{1078}{44} = r }\\\\\\\large: \: \Longrightarrow\textsf{24.5 = r}\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textbf\textcolor{magenta}{Radius of the circle = 24.5 cm}}}\\\\\\\large:\: \bigstar\textsf\textcolor{orange}{\: \: \: Area_{ ( \: Circle \: ) } = \pi r^{2} }\\\\\\\large: \: \Longrightarrow\textsf{= \cfrac{22}{7} × 24.5 ^{ 2 } }\\\\\\\large: \: \Longrightarrow\textsf{= \cfrac{22}{7} × 600.25 }\\\\\\\large: \: \Longrightarrow\textsf{= \cfrac{22}{\cancel 7 } × \cancel { 600.25 } }\\\\\\\large: \: \Longrightarrow\textsf{= 22 × 85.75}\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textbf\textcolor{magenta}{ Area _ { ( \: Circle \: ) } = 1886.5 sq. cm }}}$

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