Given:
The diameter of circular flower bed is 17 m.
It has circular sidewalk 1 m wide.
[tex]\begin{gathered} d=17 \\ r=\frac{d}{2}=\frac{17}{2}\text{ m} \end{gathered}[/tex]So, the radius circular bed with 1 m wide path is,
[tex]\begin{gathered} R=r+1 \\ =\frac{17}{2}+1 \\ =\frac{19}{2} \end{gathered}[/tex]This will form the two circles.
So, the area of the side walk is given as,
[tex]\begin{gathered} A=\pi(R^2-r^2) \\ A=\pi((\frac{19}{2})^2-(\frac{17}{2})^2) \\ =\pi\lbrack\frac{19^2}{2^2}-\frac{17^2}{2^2}\rbrack \\ =\pi\frac{\lbrack19^2-17^2\rbrack}{2^2} \\ =\pi\frac{(19+17)(19-17)}{2^2}\ldots\ldots.\ldots..(\sin ce,a^2-b^2=(a+b)(a-b)) \\ =\pi\frac{36\times2}{2^2} \\ =18\pi \\ =56.5487\text{ square meters} \end{gathered}[/tex]Answer: 56.5487 square meters.
