It is given that,

Radius of metallic sphere $=R=10.5cm$

So, its volume $=4/3\pi {{R}^{3}}=4/3\pi {{\left( 10.5 \right)}^{3}}$

We also have,

Radius of each cone $=r=3.5cm$

Height of each cone $=h=3cm$

And, its volume $=1/3\pi {{r}^{2}}h=1/3\pi {{\left( 3.5 \right)}^{2}}\left( 3 \right)$

Thus,

The number of cones $=$ Volume of metallic sphere/ Volume of each cone

$=4/3\pi {{\left( 10.5 \right)}^{3}}/1/3\pi {{\left( 3.5 \right)}^{2}}\left( 3 \right)$

$=126$