Question

find the area of a circular field whose circumference measures 2.2km​

Answer 1

Area Of Circle = 0.39 km

Step-by-step explanation:

GIVEN

Circumference Of Circle = 2.2 km

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TO FIND

Area Of Circle

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We know that,

Circumference Of Circle = 2 × π × r

2.2 = 2 × 22/7 × r

2.2 = 2 × 3.14285714 × r

2.2 = 6.28571428 × r

r = 2.2 / 6.28571428

r = 0.35

Radius = 0.35 km

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We know that,

Area Of Circle = π × r²

Area Of Circle = 22/7 × 0.35²

Area Of Circle = 3.14285714 × 0.1225

Area Of Circle = 0.39

Area Of Circle = 0.39 km

Answer 2

Given :

• Circumference of Circle = 2.2 km.

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To find :

• Area of Circular field.

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Solution :

☯ Let radius of Circle be r cm.

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We know that,

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$\star\;{\boxed{\sf{\purple{Circumference_{\;(circle)} = 2 \pi r}}}}$

Putting values,

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$:\implies\sf 2 \times \dfrac{22}{7} \times r = 2.2$

$:\implies\sf \dfrac{44}{7} \times r = 2.2$

$:\implies\sf r = 0.35$

$:\implies{\boxed{\sf{\pink{r = 0.35\;km}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Radius\;of\;circle\;is\; \bf{0.35\;km}.}}}$

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 0.35\ km}\end{picture}$

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Now, Finding area of the circular field,

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$\star\;{\boxed{\sf{\purple{Area_{\;(circle)} = \pi r^2}}}}$

$:\implies\sf \dfrac{22}{7} \times 0.35 \times 0.35$

$:\implies{\boxed{\sf{\pink{0.39\;km^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Area\;of\;circular \;field \;is\; \bf{0.39\;km^2}.}}}$

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$\boxed{\underline{\underline{\bigstar \: \bf\:Formula\:Related\:to\:Circle\:\bigstar}}}$

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$\sf (i)\;Circumference \:of\;a\;circle\; = \; \red{2 \pi r}$

$\sf (ii)\;Area\:of\;a\;circle\; = \; \pink{\pi r^2}$⠀⠀⠀⠀⠀⠀⠀

$\sf (iii)\;Length \:of\;an\;arc\;of\;a\;sector\:of\;a\;circle\;with\;radius\:r\:and\:angle\:with\:degree\;measure's \: {\theta}\:is\; = \; \green{ \dfrac{ \theta}{360^\circ} \times 2 \pi r}$

$\sf (iv)\;Area\:of\;a\;sector\; = \; \purple{ \dfrac{ \theta}{360^\circ} \times \pi r^2}$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀