a circular pond is surrounded by a 2m wide circular path. If the outer circumference of the circular path is 44m, find the inner surface of the circular path. also find the area of the path
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Answer:
Let R be radius of outer circle and r be radius of inner circle.
It has been given that 44m is the circumference of outer circle,
⇒2πR=44m
⇒2×
7
22
×R=44
⇒R=
2×
7
22
44
=
2×22
7×44
=7m
It is given that circular path is 2 m wide.
So, radius of inner circle r=R−2=7−2=5 m
So, inner circumference of path =2πr=2×
7
22
×5=31.42 m
Therefore,
Area of the path = area of outer circle - area of inner circle
⇒π(R
2
−r
2
)
=
7
22
(7
2
−5
2
)=
7
22
×24
=75.43m
2
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