For a circle to be inscribed in a square, the diameter of the circle must be equal to the side length of the square. Here, the diameter of the circle is 2 × 6 = 12 cm, which is equal to the side of the square, 12 cm. This confirms the circle is indeed inscribed in the square.

For a circle to be inscribed in a square, the diameter of the circle must be equal to the side length of the square. Here, the diameter of the circle is 2 × 6 = 12 cm, which is equal to the side of the square, 12 cm. This confirms the circle is indeed inscribed in the square.

The formula for the area of a circle is π multiplied by the square of its radius. We will use this formula to calculate the area.

Find the area of a circle of radius 6 cm inscribed in a square of side 12 cm. (E2E Verification Run: 1784956549356)

Answer: The area of the circle is $36\pi \text{ cm}^2$ .

Step-by-step solution

Step 1: Identify Given Information

We are given the radius of the circle and the side length of the square. We need to find the area of the circle.

Step 2: Verify Inscription Condition

For a circle to be inscribed in a square, the diameter of the circle must be equal to the side length of the square. Here, the diameter of the circle is $2 \times 6 = 12$ cm, which is equal to the side of the square, 12 cm. This confirms the circle is indeed inscribed in the square.

Step 3: Apply Area of Circle Formula

The formula for the area of a circle is $\pi$ multiplied by the square of its radius. We will use this formula to calculate the area.

Step 4: Calculate the Area

Substitute the given radius $r = 6$ cm into the area formula. Squaring 6 gives 36, so the area is $36\pi$ square centimeters.

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