An ice-cream novelty item consists of a cup shaped like a $3$-inch-tall frustum of a right circular cone, with a $2$-inch-diameter base at the bottom and a $6$-inch-diameter base at the top, packed solid with ice cream, together with a solid cone of ice cream of height $3$ inches whose base, at the bottom, is the top base of the frustum. What is the total volume of the ice cream, in cubic inches?

1. The frustum has height $3$ and radii $1$ and $3$. Its volume is $\frac13\pi(3)(1^2+1\cdot3+3^2)=13\pi$.
2. The cone has radius $3$ and height $3$, so its volume is $\frac13\pi(3^2)(3)=9\pi$.
3. The total volume is $13\pi+9\pi=22\pi$ cubic inches.