## Mathematical and Computing Sciences Question #90

Hunter Smith, a 11 year old male from the Internet asks on November 18, 1999,

How does the amount of air inside a soccer ball affect the distance it travels? And how is the amount of air inflated in a soccer ball determined?

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## The answer

### Barry Shell answered on November 18, 1999

The volume of a sphere is given by the formula 4/3 pi r^3, where pi is about 3.14159, and r is the radius of your soccer ball. Once you know the volume of the ball, you can figure out the volume of air in it. The mass of air will depend on its pressure, but I don't think the mass of air in the soccer ball will make much difference in the distance it travels. Of course the pressure will make a difference because an underinflated ball will behave differently when kicked due to its changed elasticity. When a ball is under inflated it will have less elastic behaviour and energy will be wasted in the collision of your foot with the ball, hence an under inflated ball should not travel as far. There are lots of websites that explain the math behind spheres, for example try the Math League for ways to calculate the volume of a sphere. Or better yet try soccer physics for a ton of fun information about the math and physics of soccer and soccer balls.

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