Prove that the area of a circular path of uniform width h surrounding

1.	Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is πh (2r + h).
Answer» Let radius of circular region = r Radius of circular path of uniform width h surrounding the circular region of radius, r = r + h Therefore area of path = π(r + h)² – πr² = πr² + πh² + 2πrh – πr² = πh (2r + h) Hence the proof.

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

Answer»

Let radius of circular region = r

Radius of circular path of uniform width h surrounding the circular region of radius,

r = r + h

Therefore area of path = π(r + h)² – πr²

= πr² + πh² + 2πrh – πr²

= πh (2r + h)

Hence the proof.