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A solid metallic sphere of diamter 16 cm is melted and recasted into smaller solid cones, each of radius 4 cm and height 8 cm. Find the number of cones so formed. - Mathematics

A solid metallic sphere of diamter 16 cm is melted and recasted into smaller solid cones, each of radius 4 cm and height 8 cm. Find the number of cones so formed.

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Solution

Diameter of the sphere, D = 16 cm

∴ Radius of sphere, R = `16/2`=8 cm

Radius of each cone, r = 4 cm

Height of each cone, h = 8 cm

Now,

Required number of cones, n

`= "Volume of sphere"/"Volume of cone"`

`= (4/3piR^3)/(1/3pir^2h)`

`= (4 xx (8)^3)/((4)^2 xx8)`

= 16

Thus, the number of cones so formed is 16

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