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A metallic sphere is melted and moulded to form conical bullets. If radius of a conical bullet is six times of its own height and the radius of the conical bullet is half of the radius of the metallic sphere, then what are the numbers of bullets formed?

A metallic sphere is melted and moulded to form conical bullets. If radius of a conical bullet is six times of its own height and the radius of the conical bullet is half of the radius of the metallic sphere, then what are the numbers of bullets formed? Correct Answer 192

Given: 

Radius of a bullet is 6 × Height of bullet 

Formula Used: 

Volume of cone = 1/3πR2H

Volume of Sphere = 4/3πR3

Calculation:

Let the height of bullet be x

Radius of bullet = 6x 

Radius of Sphere = 6x × 2 = 12x 

Volume of metallic sphere = no. of bullet × volume of 1 bullet 

⇒ 4/3π(12x)3 = n × 1/3π(6x)2x

⇒ n = 12 × 12 × 12 × 4/(6 × 6) = 192

∴ The number of bullet formed is 192

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