Count the number of soccer balls that can be accommodated on a soccer field.
- Karan Trivedi
Clarifications:
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What kind of soccer field are we seeing?
(professional artificial soccer field-fifa std, outdoor soccer field, indoor soccer field, mini football field??)
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Are we considering goal posts too?(yes)
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Shape of the goal net? Is it cubical/any other 3D shape
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What type of ball are we seeing? professional/indoor/turf/kids???
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Any dimensions in mind?
Assumptions:
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Type of field- professional soccer field.
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Dimensions: 90*45(m)-approx
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Goal post: dimensions: length=7m, breadth=3m, height= 3m
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Rectangular shape net, assuming no thickness for net
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Shape of goal net- cubical
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Shape of ball-spherical, professional soccer ball, dia=22cm
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On the soccer field without goal post, only 1 layer of ball are considered since area is considered not volume(assuming open field with nothing covered on top)
Calculation:
Area of soccer field without goalposts= 90*45 = 4050 m^2
Area of soccer ball = pi*r^2
3.14*(0.11)^2
0.038 m^2
Number of balls= area of soccer field/area of soccer ball (assumption balls are closely packed without any gaps)
Number of balls = 4050/0.038 = 106578 balls
Goals posts (balls)
Volume of goal post = l*b*h (cuboid)
7*3*3 = 63 m^3
Volume of ball= 4/3*pi*r^3 (sphere)
4/3*3.14*(0.11)^3
0.0056 m^3
Number of balls = vol of goal post/vol of ball
63/0.0056 = 11250 balls
Since there are 2 goalposts = 2*11250 = 22500 balls
Total soccer balls that can be fitted into a soccer field = 106578 + 22500 balls
Final answer = 129078 balls

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