If the circumference of a circle and the perimeter of a square are equal, then
(a) Area of the circle = Area of the square
(b) Area of the circle > Area of the square
(c) Area of the circle < Area of the square
(d) Nothing definite can be said about the relation between the areas of the circle and square
(b) 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]
$\Rightarrow \quad \frac{22}{7} r=2 a \Rightarrow 11 r=7 a$
$\Rightarrow \quad a=\frac{11}{7} r \Rightarrow r=\frac{7 a}{11}$ $\ldots($ (i)
Now, $\quad$ area of circle, $A_{1}=\pi r^{2}$
$=\pi\left(\frac{7 a}{11}\right)^{2}=\frac{22}{7} \times \frac{49 a^{2}}{121}$ [from Eq. (i)]
$=\frac{14 a^{2}}{11}$....(ii)
and area of square, $A_{2}=(a)^{2}$ ....(iii)
From Eqs. (i) and (iii), $\quad A_{1}=\frac{14}{11} A_{2}$
$\therefore \quad A_{1}>A_{2}$
Hence, Area of the circle $>$ Area of the square.