Question 32

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

To find the area of the circular garden, we first determine the radius. Since the circular garden is inscribed in a square lot with a side length of 6 meters, the diameter of the circle equals the side length of the square, which is 6 meters. Therefore, the radius is half of the diameter, resulting in a radius of 3 meters. The area of the circle is calculated using the formula \(A = \pi r^2\), which gives us \(A = \pi (3^2) = 9\pi\) square meters.

A) 6pi

This option is incorrect because it suggests that the area of the circular garden is \(6\pi\). The formula for the area requires the radius, which is 3 meters. Substituting this into the area formula yields \(9\pi\), not \(6\pi\).

B) 9pi

This option is correct as it accurately represents the area of the circular garden. With a radius of 3 meters, the area calculated using the formula \(A = \pi r^2\) results in \(9\pi\) square meters.

C) 12pi

This option is incorrect because it overestimates the area of the circular garden. The area calculation for a radius of 3 meters correctly results in \(9\pi\), and thus \(12\pi\) does not align with the derived area.

D) 36pi

This option is incorrect as it suggests a significantly larger area than what the circular garden actually has. Given the proper radius of 3 meters, the area calculated would not reach \(36\pi\) but instead is limited to \(9\pi\).

Conclusion

The area of the circular garden is definitively \(9\pi\) square meters, based on the correct application of the area formula with the radius derived from the inscribed circle's dimensions. All other options fail to provide accurate calculations based on the given radius, leading to their incorrect nature.