If a circle and a square have the same perime | vedclass

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(B) Let $r$ be the radius of the circle and $a$ be the side length of the square.Given that the perimeter of the circle equals the perimeter of the sq

Vedclass · Accepted Answer

Area of circle is larger

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(B) Let $r$ be the radius of the circle and $a$ be the side length of the square.Given that the perimeter of the circle equals the perimeter of the square:$2\pi r = 4a \Rightarrow a = \frac{\pi r}{2}$.Area of the circle = $\pi r^2$.Area of the square = $a^2 = \left(\frac{\pi r}{2}ight)^2 = \frac{\pi^2 r^2}{4}$.Comparing the areas:$\frac{	ext{Area of circle}}{	ext{Area of square}} = \frac{\pi r^2}{\frac{\pi^2 r^2}{4}} = \frac{4}{\pi}$.Since $\pi \approx 3.14$,$\frac{4}{\pi} > 1$.Therefore,the area of the circle is larger than the area of the square.

If a circle and a square have the same perimeter,then

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