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State whether it is true or false.
The area of a circular path of uniform width h surrounding a circular region of radius is $π h (2 r + h)$ .

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True

False

answer is A.

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Detailed Solution

Given that, the area of circular path of uniform width h, surrounding a circular region.
Let h be the width of the path, let r the radius of inner circle.
Radius of outer circle is (r + h).
Calculating the area of inner circle and outer circle,

Ar(Inner circle) = π r 2

and

Ar(Outer Circle) = π r + h 2

Calculating the area of the path by taking the difference of the area of outer circle and the area of inner circle,

π r + h 2 − π r 2 ⇒ π r 2 + h 2 + 2 h − π r 2

⇒ π h 2 − 2 r h

⇒ π h h + 2 r

The area of circular path of uniform width h, surrounding a circular region of radius is

π h 2 r + h

.
Hence the statement is true and correct option is 1.

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