anonymous
  • anonymous
two small parks of diameter 16m , 12 m are to be replaced by a bigger circular park. what would be the diameter of this new park, if the new park has to occupy the same space as the two small parks?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
are the two small parks squares?
anonymous
  • anonymous
small circular parks
anonymous
  • anonymous
and the options are a.30m b .20.m c.40 m d. 50m

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anonymous
  • anonymous
Well area of a circle is pi*r^2. And diameter is twice as big as the radius. So add them both up individually. pi*(16/2)^2 + pi*(12/2)^2. =pi*8^2 +pi* 6^2 =pi*64 + pi* 36 = 64pi+36pi. =100pi The total area of the two small parks is 100pi. So you need to find a new park with the same area. Area=Pi*r^2. 100pi=pi*r^2 Divide both sides by pi 100=r^2. Square root both sides r=10. And since the radius is half the distance of the diameter, you multiply it by 2. The answer is b. 20 m
dumbcow
  • dumbcow
it occupies same space so the area of the larger park must equal the sum of the smaller parks areas A = pi*r^2 park1 area = 8^2 pi = 64pi park2 area = 6^2 pi= 36pi sum = 64pi + 36pi = 100pi Area larger park = pir^2 = 100pi r^2 = 100 r=10 diameter = 20
anonymous
  • anonymous
thanks guys.....

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