Wedding cake

This is basically a stack of cylinders.

From $0\leq x < 1$ the cylinder will have a radius of 1.

From $1\leq x < 2$ the cylinder has a radius of 2.

This pattern is such that the cylinder from $n-1 \leq x < n$ will have a radius of n.

The volume of a cylinder is $\pi r^2 h$ and since each cylinder has a height of 1, it can be simplified to $\pi r^2$ .

We are looking at the volume of all the cylinders, so we are looking at

$\pi \displaystyle \sum_{r=1}^{14} r^2=\pi (1^2+2^2+3^2+...+14^2)$

Using this lemma: $\displaystyle \sum_{m=1}^n m^2=\dfrac{n(n+1)(2n+1)}{6}$

$\pi \displaystyle \sum_{r=1}^{14} r^2=\pi \cdot \dfrac{14(15)(29)}{6}=1015\pi$

$\therefore a\pi\Rightarrow \boxed{a=1015}$