Comparison of Areas: Circle vs Square

Very Hard Quantitative Comparisons Geometry Comparisons

Consider a circle with radius $r$ and a square with an inscribed circle (incircle) of the same radius $r$.

The area of the circle is given by the formula:

$$A_{circle} =\frac{22}{7}r^2$$

and the area of the square can be expressed as:

$$A_{square} = ext{side}^2 = (2r)^2 = 4r^2$$

Compare the two areas to determine the relationship.

The area of the circle is greater than the area of the square.

The area of the circle is less than the area of the square.

The areas of the circle and the square are equal.

The area of the square is unknown relative to the area of the circle.

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