Question

Prove that the area of a circular path of uniform

Answer 1

width of the path = h
radius of inner circle = r
radius of outer circle= r + h
area of the path;
= area of outer circle - area of inner circle
= λ(r + h)² - λr²
= λ( r² + h² + 2λh) - λr²
= λ(h² + 2rh) 
= λh(h+ 2r)

Answer 2

Let h be the width of the path. And we will take r to be the radius of inner circle  
The radius of the outer circle will be = (r+h) 
The area of the path will be  
= Area of outer circle – Area of inner circle  
= π(r+h) square - πr square 
= π (r square + h square + 2rh)  - π r square  
= π (h square + 2rh) =  πh(h + 2r)