Q. 195.0( 2 Votes )

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Answer :

Given:

Radius of sphere, r = 10.5 cm


Radius of cone, R = 3.5 cm


Height of cone, H = 3 cm


Let a solid sphere be melted and recasted into n smaller solid cones.


So, volume of sphere = n (Volume of cones)


We know that volume of sphere = (4πr3)/3


And Volume of cone = πr2h/3


(4πr3)/3 = n (πR2H/3)


(4π (10.5)3) / 3 = n (π (3.5)2 (3)) / 3


(4 (1157.625)) = n (36.75)


4630.5 = n (36.75)


n = 4630.5 / 36.75


n = 126


Ans. Number of cones made by melting a given solid sphere is 126.


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