Question

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

Answer 1

Area of circular region

=area of outer-area of inner circle

$=\pi {(r+h)}^2-\pi r^2$

$=\pi (r^2+h^2+2rh-r^2)$

$=\pi (h^2+2rh)$

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