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Question
A piece of wire of length 108 cm is bent to form a semicircular arc bounded by its diameter. Find its radius and area enclosed.
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Solution
Length of wire = 108 cm
Let r be the radius of the semicircle
πr+ 2r = 108
⇒ `r(pi + 2) = 108 ⇒ r(22/7 + 2) = 108`
⇒ `36/7 r = 108 ⇒ r = (108 xx 7)/36 = 21` cm
Area = `(pir^2)/2 = 22/(7 xx 2) xx 21 xx 21 = 1386/2` cm2
= 693 cm2
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