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Question
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.
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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