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?

Rationale

The area of the circular garden is 9π square meters.

Since the circular garden is inscribed in a square lot, its diameter equals the side length of the square, which is 6 meters. Therefore, the radius of the circle is half of the diameter, or 3 meters. The area of a circle is calculated using the formula A = πr², which results in an area of 9π square meters for this garden.

A (6pi) YOUR ANSWER

This option represents a miscalculation of the area based on an incorrect radius. If the radius were 6 meters, the area would indeed be 6π, but the radius derived from the inscribed circle in a square of side 6 meters is actually 3 meters, leading to a different area.

B (9pi) CORRECT

This choice accurately reflects the area of the circular garden. With a radius of 3 meters (half of the square's side length), applying the area formula A = π(3)² results in an area of 9π square meters, making this the correct answer.

C (12pi) YOUR ANSWER

Selecting this option suggests a misunderstanding of the radius. If the radius were 4 meters, then the area would be 12π. However, given that the garden is inscribed within a square of side 6 meters, the correct radius is 3 meters, leading to a smaller area.

D (36pi) YOUR ANSWER

This choice indicates a calculation based on an incorrect assumption that the radius is equal to the side length of the square. If the radius were 6 meters, the area would be 36π, but since the radius is actually 3 meters, this result does not apply to the garden's area.

Conclusion

The area of the circular garden inscribed in a square lot of side length 6 meters is correctly calculated as 9π square meters, derived from its radius of 3 meters. The other options misinterpret either the radius or area calculations, demonstrating the importance of accurately applying geometric principles in solving area-related problems.

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.

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