A circular garden is inscribed in a square lot of side length 6 meters. What is the area, in square meters, of the circular garden?
The area of the circular garden is 9π square meters.
The circular garden is inscribed in a square lot, meaning its diameter equals the side length of the square. With a side length of 6 meters, the radius of the circle is half that length, 3 meters. The area of the circle can be calculated using the formula A = πr², leading to an area of 9π square meters.
This choice represents an area calculated with an incorrect radius. If the radius were 2.45 meters (which would yield an area of about 6π), it would not correspond to the dimensions provided in the problem, where the radius is actually 3 meters.
Correctly calculated, the area of the circular garden is derived from its radius of 3 meters. Using the area formula A = πr² results in A = π(3)² = 9π square meters, confirming this as the correct answer.
This option suggests an area based on an incorrect radius of approximately 3.46 meters. If the radius were indeed 3.46 meters, the area would be calculated as A = π(3.46)², which does not align with the given dimensions from the square lot.
This choice indicates an area based on a radius of 6 meters, which would be the case for a circle equal to the side length of the square rather than inscribed within it. Since the diameter of the circle is equal to the side length of the square (6 meters), the radius must be 3 meters, making this choice incorrect.
The area of the circular garden inscribed in a square lot with a side length of 6 meters is correctly calculated as 9π square meters. The radius of the circle, being half the side length of the square, is crucial to obtaining the right area. Each of the incorrect choices arises from miscalculating the radius based on the dimensions given in the problem.
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