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(B) Let $a$ be the side of the square and $r$ be the radius of the circle.Given that the circumference of the circle is equal to the perimeter of the

Vedclass · Accepted Answer

$14: 11$

Vedclass · Answer

(B) Let $a$ be the side of the square and $r$ be the radius of the circle.Given that the circumference of the circle is equal to the perimeter of the square:$2 \pi r = 4a$$r = \frac{4a}{2 \pi} = \frac{2a}{\pi}$Now,the area of the circle is $A_c = \pi r^2$ and the area of the square is $A_s = a^2$.The ratio of the area of the circle to the area of the square is:$\frac{A_c}{A_s} = \frac{\pi r^2}{a^2} = \frac{\pi (\frac{2a}{\pi})^2}{a^2}$$= \frac{\pi \cdot \frac{4a^2}{\pi^2}}{a^2} = \frac{4}{\pi}$Substituting $\pi = \frac{22}{7}$:$= \frac{4}{22/7} = \frac{4 	imes 7}{22} = \frac{28}{22} = \frac{14}{11}$Thus,the ratio is $14: 11$.

If the circumference of a circle is equal to the perimeter of a square,what is the ratio of the area of the circle to the area of the square?

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