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Question

If a solid right circular cone of height $$24 cm$$ and base radius $$6 cm$$ is melted and recast in the shape of a sphere, then the radius of the sphere is


A
6cm
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B
4cm
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C
8cm
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D
12cm
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Solution

The correct option is B $$6 cm$$
Height of cone $$=24$$ cm 
Base of radius $$=6$$ cm
Volume of cone $$ =\cfrac { 1 }{ 3 } \pi { r }^{ 2 }h$$
$$=\cfrac { 1 }{ 3 } \times \pi \times { (6) }^{ 2 }\times 24\\ =288\pi \quad { cm }^{ 2 }$$ 
Let the radius of sphere be $$R$$ cm 
Volume of sphere $$=$$ Volume of cone 
$$\cfrac { 4 }{ 3 } \pi { R }^{ 3 }=288\pi \\ { R }^{ 3 }=\cfrac { 288\times 3 }{ 4 } =216\\ R=\sqrt [ 3 ]{ 216 } =6 \  cm$$

Mathematics

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