Q. 12

# A equally wide path runs out-side the circular field of Bakultala. The length of outer circumference exceeds the inner circumference by 132 meter. If the area of path is 14190 sq. meter, let us write by calculating the radius of circular path.

Answer :

Let R be the radius of outer circumference and r be the radius of inner circumference

Outer circumference of circular field = 2π R

And inner circumference of circular field = 2π r

Given,

Length of Outer circular field – length of inner circular field = 132m

circumference of circular field - circumference of circular field = 132 m

⇒ 2π (R- r) = 132m

⇒

⇒R – r = 21 m

This is the radius of the circular path

Given, area of path = 14190 m^{2}

⇒ π (R- r)^{2} = 14190

⇒

⇒ (R-r) = √ 4515

⇒ Radius of circular path = 67.19 m

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