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If the circumference of a circle and the perimeter of a square are equal, then which of the following statements is correct?

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Area of circle = Area of square

Area of the circle > Area of the square

Area of circle < Area of the square

Nothing definite can be said about the relation between the areas of the circle and the square.

answer is B.

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Detailed Solution

Given,
Perimeter of the square= circumference of circle
Suppose
Radius of circle bar=

r

.
Thus, the area of circle,

A = π r^{2}

.
Its circumference

= 2 πr

Let a is the side of the square. As, perimeter of the square= circumference of circle. Thus,

4 a = 2 πr

a = \frac{πr}{2}

So, Area of Square,

a^{2} = {(\frac{πr}{2})}^{2}

.
Thus, the ratio,

\frac{Area of circle}{Area of Square} = \frac{π r^{2}}{{(\frac{πr}{2})}^{2}}

\frac{Area of circle}{Area of Square} = \frac{4}{π}

\frac{Area of circle}{Area of Square} = \frac{4 \times 7}{22}

\frac{Area of circle}{Area of Square} = \frac{14}{11} > 1

Thus, area of a circle is greater than the square’s area.
Option 2 is Correct Answer.

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