Find the area of a circle of radius 6 cm inscribed in a square of side 12 cm. (E2E Verification Run: 1784956549356)
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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 2×6=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 π 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 36π square centimeters.