A circular path runs around a circular flower bed .If the circumference of the flower bed and the path are 88 m and 132 m respectively, find the width of the path and the area of the path.

Question

A circular path runs around a circular flower bed If the
circumference of the flower bed and the path are 88 m and 132 m
respectively, find the width of the path and the area of the path

Priyanka Kedia · Accepted Answer

Dear Student,

Circumference of a circle is given by 2πr, here r is the
radius

Circumference of the first circle is given as
88cm,

So 2πr = 88cm

Or 2â¨¯22/7 â¨¯r =88

Or r = 14cm

Circumference of the second circle is given as
132cm

So 2πR =132

Or 2â¨¯22/7 â¨¯R
=132

Or R = 21cm

Thus,
Width of the path=21cm-14cm = 7 cm

As these circles are concentric to each other,
Hence
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Area of the ring is given by = Area of bigger circle - area of
smaller circle

Area of a circle is given by 
πr2

Hence area of the ring = π(21)2-π(14)2

= π(212-142)

As (a2-b2

) = (a-b)(a+b)

So π(21+14)(21-14)

= 22/7 (35)(7)

= 
770cm2

Hence area of the ring is given by 
770cm2

Hope this would have clear your doubt Do let us know in case of any
further concerns