Find the area of a circular path 2m wide surrounding a circular plot of radius 16m
To find the area of the circular path surrounding the circular plot, we need to subtract the area of the circular plot from the area of the larger circle.
First, let's find the area of the circular plot. The formula for the area of a circle is:
A = π * r^2
where A is the area and r is the radius. Substituting the given radius of the circular plot (r = 16m) into the formula:
A_plot = π * (16m)^2
= π * (256m^2)
= 256π m^2
Now, let's find the area of the larger circle by adding the width of the circular path to the radius of the circular plot. The new radius will be:
r = 16m + 2m (since the circular path is 2m wide)
= 18m
Using the formula for the area of a circle:
A_path = π * r^2
= π * (18m)^2
= π * (324m^2)
= 324π m^2
Finally, to find the area of the circular path, we subtract the area of the circular plot from the area of the larger circle:
A_circular_path = A_path - A_plot
= 324π m^2 - 256π m^2
= 68π m^2
Therefore, the area of the circular path 2m wide surrounding the circular plot of radius 16m is 68π square meters.
area including path = pi (18^2)
area inside path = pi (16^2)
so area between = pi (18^2-16^2)