If the circumference of a circle and the peri | vedclass

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Question

According to the given condition,

Circumference of a circle $=$ Perimeter of square

$2 \pi r=4 a$

[where, $r$ and $a$ are radius of circle an

Vedclass · Accepted Answer

Area of the circle $>$ Area of the square

Vedclass · Answer

According to the given condition,

Circumference of a circle $=$ Perimeter of square

$2 \pi r=4 a$

[where, $r$ and $a$ are radius of circle and side of square respectively]

$\frac{22}{7} r=2 a \Rightarrow 11 r=7 a$

$a=\frac{11}{7} r \Rightarrow r=\frac{7 a}{11}$ ...........$(i)$

Now. area of circle, $A_{1}=\pi r^{2}$

$=\pi\left(\frac{7 a}{11}ight)^{2}=\frac{22}{7} 	imes \frac{49 a^{2}}{121}$ [from Eq. $(i)$]

$=\frac{14 a^{2}}{11}$ ...........$(ii)$

and area of square, $\quad A_{2}=(a)^{2}$ ...........$(iii)$

From Eqs. $(i)$ and $(iii),$ $A_{1}=\frac{14}{11} A_{2}$

$	herefore$ $A_{1}>A_{2}$

Hence, Area of the circle $>$ Area of the square.

If the circumference of a circle and the perimeter of a square are equal, then

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