Question

Find the diameter of a circle whose circumference is 66 m.​

Answer 1

`\large \bf\dag \gray{\frak{Given}}`

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• Circumference of circle = 66m.

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`\large \bf\dag \gray{\frak{To~Find}}`

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• Diameter of circle

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`\large \bf\dag \gray{\frak{Solution}}`

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To find diameter first we have to find radius of the circle.

We can find find radius of Circle by using this formula:

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`\bigstar \boxed{ \text{Circumference of circle = 2}\pi * \text{radius}}`

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Let radius be r here:

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`\dashrightarrow \sf \: Circumference \: of \: circle = 2\pi r \\`

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`\dashrightarrow \sf \:66 = 2 * (22)/(7) r \\`

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`\dashrightarrow \sf \: (66)/(2) =(22)/(7) r \\`

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`\dashrightarrow \sf \: \cancel(66)/(2) =(22)/(7) r \\`

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`\dashrightarrow \sf \:33 =(22)/(7) r \\`

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`\dashrightarrow \sf \:33 * 7 =22r \\`

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`\dashrightarrow \sf \: (33 * 7 )/(22) =r \\`

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`\dashrightarrow \sf \: \frac{ \cancel{33 }* 7 }{ \cancel{22}} =r \\`

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`\dashrightarrow \sf \: ( 3* 7 )/(2) =r \\`

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`\dashrightarrow \sf \: (21)/(2) =r \\`

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`\dashrightarrow \sf r = (21)/(2) \\`

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`\dashrightarrow \sf \boxed{ \bf \: r = 10.5m} \star`

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Now let's find diameter of circle:

We know:

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`\bigstar \boxed{ \rm \:Diameter \: of \: circle = 2 * radius}`

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So:

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`\dashrightarrow\sf \:Diameter \: of \: circle = 2 * radius \\`

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`\dashrightarrow\sf \:Diameter \: of \: circle = 2 * 10.5 \\`

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`\dashrightarrow\sf \:Diameter \: of \: circle = 2 * (105)/(10) \\`

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`\dashrightarrow\sf \:Diameter \: of \: circle = \cancel2 * \frac{105}{ \cancel{10}} \\`

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`\dashrightarrow\sf \:Diameter \: of \: circle = 1 * (105)/(5) \\`

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`\dashrightarrow\sf \:Diameter \: of \: circle = (105)/(5) \\`

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`\dashrightarrow\sf \:Diameter \: of \: circle = \cancel(105)/(5) \\`

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`\dashrightarrow \boxed{\bf\:Diameter \: of \: circle = 21m} \star\\`

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`\therefore \underline {\textsf{\textbf{Diameter of circle is equal to \red{21m}}}} \orange{\bf{\dag}}\\`