Question

A circular flower bed is 17 m in diameter and has a circular sidewalk around it 1 m wide. Find the area of the sidewalk in square meters.

Answer 1

Given:

The diameter of circular flower bed is 17 m.

It has circular sidewalk 1 m wide.

`\begin{gathered} d=17 \\ r=(d)/(2)=(17)/(2)\text{ m} \end{gathered}`

So, the radius circular bed with 1 m wide path is,

`\begin{gathered} R=r+1 \\ =(17)/(2)+1 \\ =(19)/(2) \end{gathered}`

This will form the two circles.

So, the area of the side walk is given as,

`\begin{gathered} A=\pi(R^2-r^2) \\ A=\pi(((19)/(2))^2-((17)/(2))^2) \\ =\pi\lbrack(19^2)/(2^2)-(17^2)/(2^2)\rbrack \\ =\pi(\lbrack19^2-17^2\rbrack)/(2^2) \\ =\pi((19+17)(19-17))/(2^2)\ldots\ldots.\ldots..(\sin ce,a^2-b^2=(a+b)(a-b)) \\ =\pi(36*2)/(2^2) \\ =18\pi \\ =56.5487\text{ square meters} \end{gathered}`

Answer: 56.5487 square meters.