The circumference of a given circular park is 55m.it is surrounded by a path of uniform width 3.5m.find the area of the path
r = 55/2pi
big area = pi (r+3.5)^2
little area = pi (r)^2
subtract
232
231
To find the area of the path surrounding the circular park, we need to subtract the area of the park itself from the area of the larger circle created by the path.
Let's start by finding the radius of the circular park. We know that the circumference of a circle is given by the formula:
Circumference = 2 * π * r
Given that the circumference of the park is 55m, we can rewrite the equation:
55 = 2 * π * r
Dividing both sides by 2π to isolate r, we get:
r = 55 / (2 * π)
Now, let's find the radius of the larger circle, which includes the path. The radius of the larger circle will be the radius of the park plus the width of the path on both sides. Thus:
radius of larger circle = radius of park + width of path
= r + 3.5m
Next, we can calculate the area of the larger circle, which includes both the park and the path:
Area of larger circle = π * (radius of larger circle)^2
Now, let's find the area of the park, which is represented by the smaller circle:
Area of park = π * r^2
Finally, to find the area of the path, we subtract the area of the park from the area of the larger circle:
Area of path = Area of larger circle - Area of park
Using the values we have calculated, we can substitute them into the equation and solve for the area of the path.