Solution:

Given radius of the metallic sphere, R = 10.5 cm

Volume of the sphere = (4/3)R³

= (4/3)×10.5³

= 1543.5 cm³

Radius of cone, r = 3.5 cm

Height of the cone, h = 3 cm

Volume of the cone = (1/3)r²h

= (1/3)×3.5²×3

= 12.25 cm³

Number of cones made from sphere = Volume of sphere / volume of cone

= 1543.5 /12.25

= 126

Hence the number of cones that can be made is 126.