Math, asked by rajupatelrajupatel52, 11 months ago

If the perimeter of a circle is equal to that of a square ,then find the ratio or their areal?

Answers

Answered by Sreesha
2

Answer:

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Step-by-step explanation:

2πr = 4a

πr = 2a

a = πr/2 ................

area of square, A₁ = a²

                         = π²r²/4

area of circle, A₂ = πr²

A₁ : A₂     =  π²r²/4 : πr²

               = π : 4

Answered by Anonymous
1

❏ Formula Used..

For a circle of radius r ,

\sf\longrightarrow \boxed{Area=\pi\times r{}^{2}}

\sf\longrightarrow \boxed{Perimeter=2\times\pi\times r}

For a square of side a,

\sf\longrightarrow \boxed{Area= a{}^{2}}

\sf\longrightarrow \boxed{Perimeter=4\times a}

❏ Question:-

Q) If the perimeter of a circle is equal to that of a square ,then find the ratio or their area?

Fir a circle with radius r ,

 \sf\longrightarrow Perimeter_{\red{circle}}=2\times\pi r

 \sf\longrightarrow Area_{\red{circle}}=\pi \times r{}^{2}

And, For a square of side a,

 \sf\longrightarrow Perimeter_{\red{square}}=4\times a

 \sf\longrightarrow Area_{\red{square}}=a{}^{2}

Now, according to the question perimeter of the circle is equal to the perimeter of square.

 \sf\therefore 2\times\pi r =4\times a

 \sf\longrightarrow \frac{\cancel2\times\pi r}{\cancel4} = a

 \sf\longrightarrow \frac{\pi r}{2}= a

 \sf\longrightarrow\boxed{ \red{a=\frac{\pi r}{2}}}

Therefore, the ratio of their Area.

 \sf\longrightarrow \frac{Area_{\red{circle}}}{Area_{\red{square}}}=\frac{\pi \times r{}^{2}}{a{}^{2}}

 \sf\longrightarrow \frac{Area_{\red{circle}}}{Area_{\red{square}}}=\frac{\pi \times r{}^{2}}{{\frac{\pi r}{2}}^{2}}

 \sf\longrightarrow \frac{Area_{\red{circle}}}{Area_{\red{square}}}=\frac{\pi \times r{}^{2}}{\frac{\pi{}^{2}\times r{}^{2}}{4}}

 \sf\longrightarrow \frac{Area_{\red{circle}}}{Area_{\red{square}}}=\frac{\cancel{\pi} \times \cancel{r{}^{2}}\times 4}{\cancel{\pi}\times\pi\times \cancel{r{}^{2}}}

 \sf\longrightarrow \frac{Area_{\red{circle}}}{Area_{\red{square}}}=\frac{4}{\pi}

 \sf\longrightarrow \frac{Area_{\red{circle}}}{Area_{\red{square}}}=\frac{4}{\frac{22}{7}}

 \sf\longrightarrow \frac{Area_{\red{circle}}}{Area_{\red{square}}}=\frac{\cancel4\times7}{\cancel{22}}

 \sf\longrightarrow \frac{Area_{\red{circle}}}{Area_{\red{square}}}=\frac{2\times7}{11}

 \sf\longrightarrow \frac{Area_{\red{circle}}}{Area_{\red{square}}}=\frac{14}{11}

 \sf\longrightarrow \boxed{Area_{\red{circle}}:Area_{\red{square}}=14:11}

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