SOLUTION: a circular island of diameter 100 yards is surrounded by a concentric circular moat whose area equals that of the island .which of the following best approximates the width of the

Question 234482: a circular island of diameter 100 yards is surrounded by a concentric circular moat whose area equals that of the island .which of the following best approximates the width of the moat ?
a) 20 yards b) 30 yards c) 50 yards d)70 yards e) 100 yards
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Area=pir^2=3.14*(100/2)^2=3.14*50^2=3.14*2,500=7,850 yds.^2
2*7,850=pir^2
15,700=3.14*r^2
r*2=15,700/3.14
r^2=5,000
x=sqrt5,000
x=70.71 yds. is the total radius of the island & the moat.
Width of the moat=50+x=70.71=20.71 yds. is the width of the moat.
Answer A)
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