Q3) Calculate the area and perimeter of the ring:
10 m
19 m
Answers
Step-by-step explanation:
The area of a circular ring bounded by two concentric circle of radii R and r (R > r)
= area of the bigger circle – area of the smaller circle
= πR2 - πr2
= π(R2 - r2)
= π(R + r) (R - r)
Therefore, the area of a circular ring = π(R + r) (R - r), where R and r are the radii of the outer circle and the inner circle respectively.
Solved example problems on finding the area of a circular ring:
1. The outer diameter and the inner diameter of a circular path are 728 m and 700 m respectively. Find the breadth and the area of the circular path. (Use π = 227).
Solution:
The outer radius of a circular path R = 728m2 = 364 m.
The inner radius of a circular path r = 700m2 = 350 m.
Area of a Circular Ring
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Therefore, breadth of the circular path = R - r = 364 m - 350 m = 14 m.
Area of the circular path = π(R + r)(R - r)
= 227(364 + 350) (364 - 350) m2
= 227 × 714 × 14 m2
= 22 × 714 × 2 m2
= 31,416 m2
Therefore, the area of the circular path = 31416 m2
2. The inner diameter and the outer diameter of a circular path are 630 m and 658 m respectively. Find the area of the circular path. (Use π = 227).
Solution:
The inner radius of a circular path r = 630m2 = 315 m.
The outer radius of a circular path R = 658m2 = 329 m.
Area of a Circular Path
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Area of the circular path = π(R + r)(R - r)
= 227 (329 + 315)(329 - 315) m2
= 227 × 644 × 14 m2
= 22 × 644 × 2 m2
= 28,336 m2
Therefore, the area of the circular path = 28,336 m2