A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also find area of the path.
Solution:
Consider R and r as the radius of outer and inner circle
Given
Circumference of outer circle = 44 m
As circumference = 2πR
2πR = 44
By further calculation
2 × 22/7 × R = 44
R = 44/ (2 × 22/7)
R = (7 × 44)/ (2 × 22)
R = 7 m
As r = R - 2
Substituting the value of R
r = 7 - 2
r = 5 m
Inner circumference of the circular path = 2πr
Substituting the values
= 2 × 22/7 × 5
= 31.43 m
Area of path = Area of outer circle - Area of inner circle
= π (R² - r²)
Substituting the values
= 22/7 (7² - 5²)
= 22/7 × 24
= 75.43 m²
Therefore, the inner circumference of the circular path is 31.43 m and the area of the path is 75.43 m².
✦ Try This: A circular pond is surrounded by a 4 m wide circular path. If outer circumference of circular path is 88 m, find the inner circumference of the circular path. Also find area of the path.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 110
A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also find area of the path.
Summary:
A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, the inner circumference of the circular path is 31.43 m. Also the area of the path is 75.43 m²
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