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Question

The base radius and height of a right circular solid cone are $$12 cm$$ and $$24 cm$$, respectively. It is melted and recast into spheres of diameter $$6 cm$$ each. Find the number of spheres so formed.


A
48
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B
40
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C
32
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D
24
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Solution

The correct option is C $$32$$
Radius of a right circular solid cone $$=12 cm $$
Height of a right circular solid cone $$=24 cm$$
Sphere diameter $$=6 cm$$
Volume of right circular solid cone $$=V=N \times$$ Volume of sphere
$$V=\cfrac 13 \pi { r }^{ 2 }h=N\times \cfrac { 4 }{ 3 } \pi { r }^{ 3 }$$
$$\cfrac 13 \times { 12 }^{ 2 }\times 24=N\times \cfrac { 4 }{ 3 } { 3 }^{ 3 }$$
$$N=32$$

Mathematics

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