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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
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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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