Three solid metallic spheres of radii $6$, $8$ and $10$ centimetres are melted to form a single solid sphere. The radius of the sphere so formed is __________.

Using the sphere volume formula V = (4/3) * pi * r^3, the volumes of the three spheres are (4/3) * pi * 6^3, (4/3) * pi * 8^3, and (4/3) * pi * 10^3, which sum to a total volume of (4/3) * pi * (216 + 512 + 1000) = (4/3) * pi * 1728. Setting this equal to the volume of the new sphere, (4/3) * pi * R^3 = (4/3) * pi * 1728, gives R^3 = 1728. Taking the cube root reveals the radius of the new sphere is 12 cm. The result is 12 cm.

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