Question

Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is $\pi h(2r+h)$.

Answer 1

Inner radius = r

Outer radius = r + h

So, area of the path $=\pi (r+h{)}^2-\pi r^2$

$=\pi \left[\right(r+h{)}^2-r^2]$

$=\pi (r+h+r)(r+h-r)$

$=\pi h(2r+h)$