A solid metallic sphere of radius 10.5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height 3 cm. Find the number of cones so formed.

Updated on June 1, 2025 | By Learnzy Admin

First, find the volume of the original metallic sphere.
The formula for the volume of a sphere is:
V = (4/3) × π × r³
Radius of the sphere = 10.5 cm

So, V = (4/3) × π × (10.5)³ = (4/3) × π × 1157.625  =  4851.375 cm³

Next, find the volume of one small cone.
The formula for the volume of a cone is:
V = (1/3) × π × r² × h
Radius = 3.5 cm, Height = 3 cm
V = (1/3) × π × (3.5)² × 3 = π × 12.25 ≈ 38.48 cm³

Now, divide the volume of the sphere by the volume of one cone:
Number of cones = 4851.375 ÷ 38.48 ≈ 126

Hence the number of cones formed 126 

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