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Question
A circular path has to be constructed around a circular lawn. If the outer and inner circumferences of the path are 88 cm and 44 cm respectively, find the width and area of the path
Solution
Outer circumference of the circular lawn = 88 cm
2πR = 88 cm
Inner circumference of the lawn 2πr = 44 cm
2πR – 2πr = 88 – 44
`2 xx 22/7 ("R" - "r")` = 44
(R – r) = `(44 xx 7)/(2 xx 22)`
Outer radius – Inner radius = 7 cm
∴ Width of the lawn = 7 cm
Also 2πR + 2πr = 88 + 44
2π(R + r) = 132
π(R + r) = `132/2`
= 66 cm
Area of the path = πR2 – πr2 sq.units
= π(R + r)(R – r)
= 66 × 7
Area of the path = 462 cm2
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