A solid metal sphere of radius 10.5 cm is melted and recast into small solid cones, each of radius 3.5 cm and height 3 cm. How many such cones are obtained?

Sphere = (4/3)π$(10.5{)}^3$ = (4/3)π $x$ 1157.625 = 1543.5π cubic cm. Each cone = (1/3)π$(3.5{)}^{2}x$ 3 = 12.25π cubic cm. Melting conserves volume, so the count = 1543.5π/12.25π = 126. The trap 42 treats each cone as a cylinder, forgetting the 1/3; 63 uses the hemisphere volume (2/3)π$r^3$ for the sphere; 378 uses 4π$r^3$, dropping the 3 in the denominator of 4/3.