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Question

A metallic sphere of radius 10.5cm is melted and then recast into small cones each of radius 3.5cm and height 3cm. The number of such cones is

A
63
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B
126
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C
21
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D
130
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Solution

The correct option is D 126
Radius of sphere (r)=10.5cm=212cm
Volume =43πr3=43π×212×212×212
Let n cones are formed
Radius of cone (R)=3.5cm=72cm
Height of cone (h)=3cm
Volume of 1 cone =13πR2h
=13π×72×72×3=494π
Volume of n cones =49nπ4
Vol. of cylinder = Vol. of n cones
4π3×212×212×212=49nπ4
n=2×3×21
n=126 cones.


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