Answer: To find the area of the walkway surrounding the circular garden, we need to subtract the area of the circular garden from the area of the larger circle that includes the garden and the walkway.
The diameter of the larger circle is equal to the diameter of the garden plus the width of the walkway on both sides, which is 1 meter on each side. So the diameter of the larger circle is:
10 + 1 + 1 = 12 meters
The radius of the larger circle is half of its diameter, which is:
12 / 2 = 6 meters
The area of the larger circle is:
πr^2 = π(6)^2 = 36π square meters
The radius of the circular garden is half of its diameter, which is:
10 / 2 = 5 meters
The area of the circular garden is:
πr^2 = π(5)^2 = 25π square meters
Therefore, the area of the walkway surrounding the circular garden is the difference between the area of the larger circle and the area of the circular garden:
Area of walkway = Area of larger circle - Area of circular garden
= 36π - 25π
= 11π square meters
So the area of the walkway is 11π square meters.