Question

The area of a circular path of uniform width h surrounding a circular region of radius r is 

पर्याय

• \[\pi(2r + h)r\]

• \[\pi(2r + h)r\] 

• \[\pi(2r + h)h\]

• \[\pi(h + r)r\] 

• \[\pi(h + r)h\] 

Answer 1

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`