If the perimeter of a circle is equal to that | vedclass

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Question

(C) Let the radius of the circle be $r$ and the side of the square be $a$.According to the given condition,Perimeter of a circle = Perimeter of a squa

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$14: 11$

Vedclass · Answer

(C) Let the radius of the circle be $r$ and the side of the square be $a$.According to the given condition,Perimeter of a circle = Perimeter of a square$2 \pi r = 4a \Rightarrow a = \frac{\pi r}{2}$ ...............$(i)$Now,the ratio of their areas is:$\frac{	ext{Area of circle}}{	ext{Area of square}} = \frac{\pi r^2}{a^2} = \frac{\pi r^2}{(\frac{\pi r}{2})^2}$ [from Eq. $(i)$]$= \frac{\pi r^2}{\frac{\pi^2 r^2}{4}} = \frac{4}{\pi} = \frac{4}{\frac{22}{7}} = \frac{4 	imes 7}{22} = \frac{28}{22} = \frac{14}{11}$Thus,the ratio of their areas is $14: 11$.

If the perimeter of a circle is equal to that of a square,then the ratio of their areas is

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