A circular path of uniform width of area 500.5 m2 is made around a circular park of area 1386 m2. If a plant is planted after every 2m on both sides of the circular path, how many total numbers of plants are planted on the path?
A circular path of uniform width of area 500.5 m2 is made around a circular park of area 1386 m2. If a plant is planted after every 2m on both sides of the circular path, how many total numbers of plants are planted on the path? Correct Answer 143
Given:
Area of circular park = 1386 m2
Area of circular path = 500.5 m2
Formula used:
Area of circle = π × (radius)2
Perimeter of circular path = 2π(R + r)
Calculation:
The circular path is in the form of a circular ring around the park, as shown below, where ‘r’ is the radius of the circular park and ‘R’ is the radius of the circular park and the path,
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Area of circular park = 1386 m2
∵ Area of circle = π × (radius)2
⇒ Radius of circular park = r = √(1386/π) = √(1386 × 7/22) = √441 = 21 m
Also, area of circular path = 500.5 m2
⇒ Total area of park & path = 1386 + 500.5 = 1886.5 m2
⇒ Radius of park & path = R = √(1886.5 × 7/22) = √600.25 = 24.5 m
Now,
Perimeter of circular path = 2π(R + r) = 2 × 22/7 × 45.5 = 286 m
A plant is planted after every 2 m on both sides of the circular path,
∴ Total no. of plants planted = 286/2 = 143
