Q$\mathrm{.}3)$ In casting experiments performed using a titanium alloy and a zircon sand mold, it took $155$ s for a cubeshaped casting to solidify. The cube was $50$ mm on a side. If the same alloy and mold type were used, find the total solidification time for a cylindrical casting in which the diameter $=30mm$ and length $50$ mm $.$

Q$\mathrm{.}4)$ A resistance spot welding operation is performed on two pieces of $1\mathrm{.}5$ mm thick sheet steel using $12000$ A for a $0\mathrm{.}2$ sec duration.. The electrodes are $7$ mm in diameter at the contacting surfaces, resistance is assumed to be $0\mathrm{.}0001$ ohm $,$ and the resulting weld nugget is a sphere of a $6$ mm in diameter. The unit melting energy for the metal $U=12\mathrm{.}0\frac{J}{m}m3.$ What portion of the heat generated was used to form the weld nugget and what portion was dissipated in to the work metal, electrodes and surrounding air.