The area of the circle that can be inscribed in a square of side 6 cm is
\(36\pi\,\text{cm}^2\)
\(18\pi\,\text{cm}^2\)
\(12\pi\,\text{cm}^2\)
\(9\pi\,\text{cm}^2\)
Step 1: A circle inscribed in a square touches all four sides of the square. That means the diameter of the circle is equal to the side of the square.
Step 2: Side of the square is given as \(6\,\text{cm}\). So, diameter of the circle = \(6\,\text{cm}\).
Step 3: Radius is half of the diameter. Radius \(r = \tfrac{6}{2} = 3\,\text{cm}\).
Step 4: Formula for the area of a circle is \(A = \pi r^2\).
Step 5: Substitute \(r = 3\,\text{cm}\): \(A = \pi \times 3^2 = 9\pi\,\text{cm}^2\).
Final Answer: The area of the circle is \(9\pi\,\text{cm}^2\). Therefore, the correct option is (D).