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  • 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

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 thecircle and square.

Answers (1)

(B) Area of the circle > Area of the square

Solution

circumference of a circle=2\pi r

Let the radius of the circle = r

perimeter of a square =4 \times side

let the side of a square = a

According to question

circumference of a circle = perimeter of a square
 \\ 2 \pi r=4a\\ \pi r=2a\\\\ a=\frac{\pi r}{2}\\\\ \therefore \frac{Area \; of \; circle}{Area \; of\; square}=\frac{\pi r^{2}}{\left (\frac{\pi r}{2} \right )^{2}}=\frac{\pi r^{2}}{\pi r^{2}}\times \frac{4}{\pi}=\frac{4 \times 7}{22}=\frac{14}{11}

And \frac{14}{11}> 1

Hence Area of the circle > Area of the square.

Posted by

infoexpert24

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