Question

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Answer 1

Answer:

answer is 14:11

Step-by-step explanation:

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Answer 2

Answer:

14 : 11

Step-by-step explanation:

We are given that Perimeter of circle = Perimeter of square

We need to find ${\dfrac{\textbf{Area of circle}}{\textbf{Area of square}} }$

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[1] Perimeter of circle

Let the radius of the circle of r.

Perimeter of circle (circumference) = 2πr ---(1)

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[2] Perimeter of square

Let the length of side of the square be a.

Perimeter of square = 4 × Side = 4a ---(2)

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Now equating equation (1) and (2)

Perimeter of circle = Perimeter of square

⇒ 2πr = 4a

$\sf {\implies r = \frac{4a}{2 \pi}}$

$\sf {\implies r = \frac{2a}{\pi}}$

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[3] Area of circle

Area of circle = πr²

$\sf{\displaystyle = \pi \bigg(\frac{2a}{\pi}\bigg)^2}$

$\sf{= \pi \times \dfrac{2a}{\pi} \times \frac{2a}{\pi}}$

$\sf{ = \dfrac{4a^2}{\pi}}$

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[4] Area of square

Area of square = Side²

= a²

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Now,

$\bigstar \; {\dfrac{\textbf{Area of circle}}{\textbf{Area of square}} }$

$\sf{= \dfrac{\frac{4a^2}{\pi}}{a^2}}$

$\sf{=\dfrac{4a^2}{\pi} \times \dfrac{1}{a^2}}$

$= \sf \dfrac{4}{\pi}$

$= \sf \dfrac{4}{\frac{22}{7}} \quad \bigg[\pi = \dfrac{22}{7}\bigg]$

$= \sf 4 \times \dfrac{7}{22}$

$\sf = 14 : 11$

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