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The area of the circle that can be inscribed in a square of side $6$ cm is

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4 π {cm}^{2}

6 π {cm}^{2}

8 π {cm}^{2}

9 π {cm}^{2}

answer is D.

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Detailed Solution

Given that, side of square is 6cm.
To inscribe a circle inside a square, the centre coincides and the diameter of the circle is equal to the side of square
Let the radius of circle be ‘r’.
Diameter of inscribed circle = Side of square

\Rightarrow

2r = 6

\Rightarrow

r = 3 cm
Now,
Area of circle =

{πr}^{2}

\Rightarrow Area of circle = 3^{2} π

\Rightarrow Area of circle = 9 π {cm}^{2}

Thus, the area of circle inscribed in square of side 6cm is

9 π {cm}^{2}

.
Therefore, option (4) is correct.

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