A metal has FCC crystal structure with $2.71 \mathrm{~g} / \mathrm{cm}^3$ of density and $26.98 \mathrm{~g} / \mathrm{mol}$ of atomic weight. The Avogadro's number is $6.023 \times 10^{23}$. The atomic radius of the metal is
$\_\_\_\_$ nm (rounded off to 2 decimal places).
$$ \text { Match the mold elements in the casting process with the most suitable function } $$
| Column I | Column II | ||
|---|---|---|---|
| P. | Blind riser |
I. | Casting with internal cavity |
| Q. | Chill |
II. | Molten metal reservoir |
| R. | Skim bob |
III. | Nucleating agent |
| S. | Core |
IV. | Assisting in faster heat removal from melt |
| T. | Insulating sleeve |
V. | Removal of impurities |
| U. | Inoculant | VI. | Increasing the solidification time |
Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidification time of the cube to that of the cylinder is ___________ (rounded off to 2 decimal places).
Assume that solidification time follows Chvorinov's rule with an exponent of 2 .
Aluminium is casted in a cube-shaped mold having dimensions as 20 mm × 20 mm × 20 mm. Another mold of the same mold material is used to cast a sphere of aluminium having a diameter of 20 mm. The pouring temperature for both cases is the same. The ratio of the solidification times of the cube-shaped mold to the spherical mold is _______ (answer in integer).
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