# Number of Tennis Balls to make a 4 sided pyramid of 25 levels

# Answer : 5525 Balls

Start from the top of the pyramid.
For a pyramid of 1 level - Number of Tennis balls required is 1
For a pyramid of 2 level - Number of Tennis balls required is 1 + 4
For a pyramid of 3 level - Number of Tennis balls required is 1 + 4 + 9
For a pyramid of 4 level - Number of Tennis balls required is 1 + 4 + 9 + 16
How do you go about doing this is each level of N balls requires N+1 balls as support in the case of 2 dimensional pyramid, since this has 3 dimensions, each N^{2} ball requires support from (N+1)^{2} ,
therefore there would be N^{2} Balls in N^{th} level where N is 1,2,3,4... 25. So the answer here is
1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + .... + 25^{2}
Using this formula to calculate the sum of squares of first N integers , we can calculate the number of balls requires as
## (25 x (26) x (51) ) / 6 = 5525

10 Dec, 2009

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