504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere.

Given, 

diameter of each cone = 3.5 cm

radius, r = 3.5/2

height of each cone = 3cm

Thus the volume of each cone, V = 1/3 πr2h

= 1/3 π (3.5/2)2.3

= 1/3 x 22/7 x 3.5/2 x 3.5/2 x 3

= 19.25/2 cu.cm.

Volume of 504 cones = 504 x 19.25/2 = 4851 cu.cm.

As per given condition, 504 cones are melted to form a sphere. Thus, the volume of 504 cones and sphere made from them will be same.

Hence,

Volume of sphere = 4851 cu.cm.

4/3 π r3 = 4851

r3 = (4851 x3)/(4xπ)

r = 10.5

Therefore, the diameter of sphere is, d = 2 x 10.5 = 21cm.

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