Final answer:
The area of the path, which is 4 meters wide and surrounds a circular flower bed with a diameter of 66 meters, is calculated to be 881.1 square meters.
Step-by-step explanation:
To calculate the area of the path surrounding a circular flower bed, we first need to determine the diameter of the entire area including the path, which will be the diameter of the flower bed plus twice the width of the path.
Next, we calculate the areas of both the larger circle (flower bed plus path) and the smaller circle (flower bed alone), and find the difference between them. This difference is the area of the path.
The diameter of the flower bed is given as 66 meters. The width of the path is 4 meters.
Therefore, the diameter of the whole area including the path is 66 meters + 2 × 4 meters = 74 meters.
The radius of the larger area is half of the diameter, so 74 meters / 2 = 37 meters.
The radius of the smaller circle is half of 66 meters, which is 33 meters.
Now we can use the formula for the area of a circle, A = πr², to calculate the areas. For the larger circle (including the path), the area is π × (37 meters)² = π × 1369 square meters = 4302.3 square meters (approximated to one decimal place).
For the smaller circle (just the flower bed), the area is π × (33 meters)² = π × 1089 square meters = 3421.2 square meters (approximated to one decimal place).
The area of the path is the area of the larger circle minus the area of the smaller circle, which is 4302.3 square meters - 3421.2 square meters = 881.1 square meters.