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

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WindyMintidn

[tex] \large \bf\dag \gray{\frak{Given}}[/tex]

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  • Circumference of circle = 66m.

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[tex] \large \bf\dag \gray{\frak{To~Find}}[/tex]

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  • Diameter of circle

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[tex] \large \bf\dag \gray{\frak{Solution}}[/tex]

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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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[tex] \bigstar \boxed{ \text{Circumference of circle = 2}\pi \times \text{radius}}[/tex]

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Let radius be r here:

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[tex] \dashrightarrow \sf \: Circumference \: of \: circle = 2\pi r \\ [/tex]

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[tex] \dashrightarrow \sf \:66 = 2 \times \dfrac{22}{7} r \\ [/tex]

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[tex] \dashrightarrow \sf \: \dfrac{66}{2} =\dfrac{22}{7} r \\ [/tex]

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[tex] \dashrightarrow \sf \: \cancel\dfrac{66}{2} =\dfrac{22}{7} r \\ [/tex]

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[tex] \dashrightarrow \sf \:33 =\dfrac{22}{7} r \\ [/tex]

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[tex] \dashrightarrow \sf \:33 \times 7 =22r \\ [/tex]

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[tex] \dashrightarrow \sf \: \frac{33 \times 7 }{22} =r \\ [/tex]

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[tex] \dashrightarrow \sf \: \frac{ \cancel{33 }\times 7 }{ \cancel{22}} =r \\ [/tex]

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[tex] \dashrightarrow \sf \: \frac{ 3\times 7 }{2} =r \\ [/tex]

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[tex] \dashrightarrow \sf \: \frac{21}{2} =r \\ [/tex]

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[tex] \dashrightarrow \sf r = \frac{21}{2} \\ [/tex]

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[tex] \dashrightarrow \sf \boxed{ \bf \: r = 10.5m} \star[/tex]

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Now let's find diameter of circle:

We know:

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[tex] \bigstar \boxed{ \rm \:Diameter \: of \: circle = 2 \times radius}[/tex]

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So:

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[tex] \dashrightarrow\sf \:Diameter \: of \: circle = 2 \times radius \\ [/tex]

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[tex] \dashrightarrow\sf \:Diameter \: of \: circle = 2 \times 10.5 \\ [/tex]

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[tex] \dashrightarrow\sf \:Diameter \: of \: circle = 2 \times \dfrac{105}{10} \\ [/tex]

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[tex] \dashrightarrow\sf \:Diameter \: of \: circle = \cancel2 \times \dfrac{105}{ \cancel{10}} \\ [/tex]

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[tex] \dashrightarrow\sf \:Diameter \: of \: circle = 1 \times \dfrac{105}{5} \\ [/tex]

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[tex] \dashrightarrow\sf \:Diameter \: of \: circle = \dfrac{105}{5} \\ [/tex]

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[tex] \dashrightarrow\sf \:Diameter \: of \: circle = \cancel\dfrac{105}{5} \\ [/tex]

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[tex] \dashrightarrow \boxed{\bf\:Diameter \: of \: circle = 21m} \star\\ [/tex]

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[tex]\therefore \underline {\textsf{\textbf{Diameter of circle is equal to \red{21m}}}} \orange{\bf{\dag}}\\ [/tex]

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