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Question
A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. The number of such cones is
Options
63
126
21
130
Solution
Radius of metallic sphere = 10.5 cm
Therefore,
Volume of the sphere
`=4/3pir^3`
`=4/3 xx pi xx 10.5 xx 10.5 xx 10.5`
`= (4630.5pi)/3 ................(1)`
Now,
Radius of the cone = 3.5 cm
and Height of the cone = 3 cm
Therefore,
Volume of the cone
`=1/3 pir^2 h`
`=1/3 xx pi xx 3.5 xx 3.5 xx 3`
`=(36.75pi)/3 .......... (2)`
Number of cone = `"volume of sphere"/ "volume of cone"`
Dividing eq. (1) and (2) we get
Number of cone `= ((4630.5 pi)/3)/((36.75 pi)/3) = 126`
Number of cone = 126
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