A metallic sphere of radius 10.5 cm is melted and then recast into small cones…

Step 1: Identify given dimensions.

Radius of sphere (R) = 10.5 cm Radius of cone (r) = 3.5 cm Height of cone (h) = 3 cm

Step 2: Write volume formulas.

Volume of sphere = (4/3) * π * R^3 Volume of cone = (1/3) * π * r^2 * h

Step 3: Equate volumes to find number of cones (n).

n * (1/3) * π * r^2 * h = (4/3) * π * R^3 n = (4 * R^3) / (r^2 * h)

Step 4: Substitute values and calculate.

n = (4 * 10.5^3) / (3.5^2 * 3) n = (4 * 1157.625) / (12.25 * 3) n = 4630.5 / 36.75 n = 126

The number of cones formed is 126.