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in Surface Areas And Volumes by (56.3k points)

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.

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Best answer

Given,

Radius of metallic sphere = R = 10.5 cm

So, its volume = 4/3 πR3 

= 4/3 π(10.5)3

We also have,

Radius of each cone = r = 3.5 cm

Height of each cone = h = 3 cm

And, its volume = 1/3 πr2

= 1/3 π(3.5)2(3)

Thus,

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

= 4/3 π(10.5)3 / 1/3 π(3.5)2(3)

= 126

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