Question $2$

A cylindrical riser with diameter$-$to$-$length ratio $1\mathrm{.}0$ is to be designed for a sand casting mold. The casting geometry is illustrated in Figure Q$1,$ in which the units are inches. If the mold constant in Chyorinoy's rule $19\mathrm{.}5mi\frac{n}{i}{n}^2,$ determine the dimensions of the riser so that the riser will take $0\mathrm{.}5$ min longer to freeze than the casting itself.

Fig Q$1$