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
B
4cm
C
8cm
D
12cm

Solution

## The correct option is B $$6 cm$$Height of cone $$=24$$ cm Base of radius $$=6$$ cmVolume 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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