Question

The circumference of a given circular park is 55 m. It is surrounded by a path of uniform width of 3.5 m. Find the area of the path.

Answer 1

Let r be the radius of the circular park.
2πr = 55
r = `55/2π`
  = 8.75 m

area of the park = π x ( 8.75 )² = 240.625 m² 

Radius of the outer circular region including the path is given by
R = 8.75 + 3.5
   = 12.25 m

Area of that circular region is A = π x ( 12.25 )² = 471.625 m² 
Hence area of the path is given by 
Area of the path = 471.625 - 240.625 = 231 m².