A circular flower bed is surrounded by a path 4m wide . the diameter of the flower bed is 66m . what is the area of this path
To find the area of the path surrounding the circular flower bed, we need to subtract the area of the flower bed from the area of the larger circle formed by the path.
First, let's find the radius of the flower bed. The diameter of the flower bed is given as 66m, so we can divide it by 2 to find the radius:
Radius = Diameter / 2 = 66m / 2 = 33m
Next, let's find the area of the flower bed. The area of a circle is given by the formula:
Area = π * r^2
Where π is a constant approximately equal to 3.14159 and r is the radius. Substituting the values:
Area of flower bed = π * (33m)^2
Now, let's find the area of the larger circle formed by the path. To do this, we need to add twice the width of the path to the diameter of the flower bed to find the diameter of the larger circle:
Diameter of larger circle = Diameter of flower bed + 2 * Width of path
= 66m + 2 * 4m
= 66m + 8m
= 74m
We can then find the radius of the larger circle:
Radius of larger circle = Diameter of larger circle / 2
= 74m / 2
= 37m
Now, let's find the area of the larger circle:
Area of larger circle = π * (37m)^2
Finally, we can find the area of the path by subtracting the area of the flower bed from the area of the larger circle:
Area of path = Area of larger circle - Area of flower bed
Therefore, the area of the path surrounding the circular flower bed is equal to the difference between the area of the larger circle and the area of the flower bed.
radius of flower bed --- r m
2πr = 66
r = 33/π
radius of whole thing = 4+33/π
area of whole thing = π(4+33/π)^2
area of flower bed =π(33/π)^2
subtract the two areas to get the area of the path.
you do the arithmetic