Asked by Sara
Suppose you have 100ft of fence to make a play area for your dog. Does a square or circle provide more area? What other factors might you take into consideration in designing your play area?
Answers
Answered by
Reiny
The circle is the most efficient shape for a maximum area given some perimeter.
Here is why:
if circumf = 100
2πr = 100
r = 100/(2π) = 15.915
area = πr^2 = π(15.915)^2 = 795.77
if you had a square:
each side = 25
Area = 25x25 = 625 which is quite a bit less than the circle
Any other shape, e.g. an equilateral triangle, is less than the area of a circle.
Here is why:
if circumf = 100
2πr = 100
r = 100/(2π) = 15.915
area = πr^2 = π(15.915)^2 = 795.77
if you had a square:
each side = 25
Area = 25x25 = 625 which is quite a bit less than the circle
Any other shape, e.g. an equilateral triangle, is less than the area of a circle.
Answered by
Alicia
Circle it has a larger area by 3 more
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