Answer: [tex]216.76 m^{2}[/tex]
Explanation:
Assuming the shape of the circular flower bed with its sidewalk is as shown in the figure, where the flower bed is the inner white circle and the sidewalk is the black part; we have to circles, hence two areas:
[tex]A_{1}=\pi R^{2}[/tex] (1)
And:
[tex]A_{2}=\pi r^{2}[/tex] (2)
Where:
[tex]A_{1}[/tex] is the area of the outer circle
[tex]A_{2}[/tex] is the area of the inner circle
[tex]r=\frac{diameter}{2}=\frac{20 m}{2}=10 m[/tex] is the radius of the inner white circle
[tex]R=10 m+ 3 m=13 m[/tex] is the radius of the outer black circle
So, the area of the sidewalk will be:
[tex]A=A_{1}-A_{2}[/tex] (3)
Substituting (1) and (2) in (3):
[tex]A=\pi R^{2}-\pi r^{2}[/tex] (4)
[tex]A=\pi (R^{2}-r^{2})[/tex] (5)
Solving with the given data:
[tex]A=\pi ((13 m)^{2}-(10 m)^{2})[/tex] (6)
[tex]A=\pi ((13 m)^{2}-(10 m)^{2})[/tex] (7)
Finally:
[tex]A=216.76 m^{2}[/tex] This is the area of the sidewalk
