Chapter 4.3, Problem 69ES

To determine

To calculate: The value of $N\left(3\right)$ using the function and the figure, and the number of oranges in a pyramid with $5$ layers if the Kepler Conjecture is that the most effective way to pack spheres is in the shape of a square pyramid. The number N of balls in the stack is given by the polynomial function $N\left(x\right)=\frac{1}{3}{x}^3+\frac{1}{2}{x}^2+\frac{1}{6}x$, where $x$ is the number of layers. Consider the figure which is shown below,