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Question
The area of a circular path of uniform width h surrounding a circular region of radius r is
Options
\[\pi(2r + h)r\]
\[\pi(2r + h)r\]
\[\pi(2r + h)h\]
\[\pi(h + r)r\]
\[\pi(h + r)h\]
Solution
We have
`OA=r`
`AB=h`
Therefore, radius of the outer circle will be.`r+h`
Now we will find the area between the two circles.
∴Area of the circular path=`pi(r+h)^2-pir^2`
∴Area of the circular path=`pi(r^2+2rh+h^2)-pir^2`
∴Area of the circular path=`pi(r^2+2rh+h^2-r^2)`
Cancelling `r^2 "we get"`
∴Area of the circular path=`pi(2rh+h^2)`
∴Area of the circular path=`pi(2r+h)h`
Therefore,are of the circle is `pi(2r+h)h`
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