Question

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

Answer 1

Answer:

Step-by-step explanation:

Answer:

πh(2r + h)

Step-by-step explanation:

Please see the attached diagram for the problem description.  

We are measuring the circular path colored in the diagram.  

Inner Circle radius is r.  

Since the road width is h, the outer circle radius is (r + h)

Area of outer circle = π(r + h)^2

Area of inner circle = πr^2

Area of circular path = area of outer circle – area of inner circle

= π(r + h)^2 – πr^2

= π[(r + h)^2 – r^2]

= π[(r + h + r)(r + h – r)]       (Since a^2 – b^2 = (a + b)(a - b)]

= π(2r + h)(h)

= πh(2r + h)

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Answer 2

Answer:

πh(h+r)

Step-by-step explanation:

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