Q $1.$ A cylindrical riser is to be designed for a sand casting mold. The length of the cylinder is to be $2$ times its diameter. The casting is a square plate, each side $a=30cm$ and thickness $h=15cm.$ If the metal is cast iron, and the mold constant in Chvorinov's rule $=2\mathrm{.}50mi\frac{n}{c}{m}^2,$ determine :

a$)$ the length of riser so that it will take $25\%$ longer for the riser to solidify

b$)$ the size of the pattern for this casting by assuming only shrinkage allowance