a metallic sphere of radius 10 5 cm is melted and recast..., Area & Volume, General Mathematics

Question:A metallic sphere of radius `10.5 cm is melted and recast into small cones, each of radius `3.5` cm and height `3` cm. The number of such cones will be :

A `21` 
B `63` 
C `126` 
D `130`

/113

+ AnswerC

+ ExplanationVolume of sphere 

`= (4/3 π xx 21/2 xx 21/2 xx 21/2) cm^3`

`= (3087 π)/2 cm^3.`

VOlume of each cone 

`= (1/3 π xx 7/2 xx 7/2 xx 3) cm^3`

`= (49 π)/4 = cm^3.`

:. Number of `2` cones

`= ((3087 π)/2 xx 4/(49 π))`

`= 126.`

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