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Question -

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.



Answer -

Given,

Radius of metallicsphere = R = 10.5 cm

So, its volume = 4/3πR3 = 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 = 1/3πr2h = 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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