How Many Cricket Balls Are In The Pyramid?

Geometry Level 4

Vini is the manager of a sports store. Coming into work, he saw that the competing store down the block made a huge 1.5 m tall square pyramid of cricket balls, which was attracting attention from pedestrians. The pyramid consists of several layers of balls: the topmost layer with 1 ball, the next one with 4 balls, the next one with 9 balls, and so on.

Not to be outdone, Vini wants to construct a larger display that is at least 1.8 m tall. He knows that the diameter of a cricket ball is 7 cm and that each box in the warehouse contains 100 cricket balls. What is the minimum number of boxes that are needed to build the pyramid?

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