# How to fill a car with tennis balls

if i want to fill interior of a car with tennis balls how many will be required.

How to calculate this?

if we are provided with length,breadth,height of car(height varies at each part) and radius of tennis ball.

Some one please explain it in detail.

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I removed the "logic" tag. – Carl Mummert Feb 8 '13 at 11:45
Do you know calculus? Multivariable Calculus? Do you have any idea what shape the car's roof is? You say height varies, so we will have to assume the base is a rectangle. Do you have an equation that describes, parametrizes the roof? With only this your question is incomplete. – user45099 Feb 8 '13 at 11:54
I know this can not be solved with out knowing the shape structure.I just want to how it can be solved. – kevin Feb 8 '13 at 12:08
A crude approximation would be to divide the volume of the car $lbw$ by the volume of a tennis ball $4\pi r^3 / 3$ and multiply by an appropriate sphere packing density. Let's say: $0.75*lbw / (4\pi r^3 / 3)$. – anthus Feb 8 '13 at 12:12

Alright, first of all you should try to work the volume of the car and the volume of the balls and figure it out by there. In trying to figure the volume of the car, you can seperate the car into pieces and work your way through there. However, this will not give you a correct answer in the real life. While trying to figure out the volume of the balls, you should consider the best possible combination in which you can put them. Because in whatever way you combine them, there will be some spaces between them, and this will cause the mistake in the previous calculation. For this combination thing, I suggest you looking at packaging ratio. http://mathworld.wolfram.com/SpherePacking.html I hope this would help you.

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