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Question

The diameter of a metallic sphere is $$6 cm$$. It is melted and drawn into a wire of diameter $$2 cm$$, then the length of the wire is


A
12cm
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B
18cm
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C
36cm
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D
66cm
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Solution

The correct option is B $$36 cm$$
Diameter of sphere $$=6$$ cm
Radius of sphere $$=\cfrac { 6 }{ 2 } =3cm$$
Volume of sphere $$=\cfrac { 4 }{ 3 } \pi { r }^{ 3 }\\ =\cfrac { 4 }{ 3 } \pi \times 3\times 3\times 3\\ =36\pi  { cm }^{ 3 }$$

Let the length of wire be $$h$$ cm
Diameter of wire $$=2$$ cm
Radius of wire $$=\cfrac { 2 }{ 2 } =1 cm$$
As the wire is in the shape of cylinder .so that volume of cylinder $$=\pi { r }^{ 2 }h$$
Now, volume of metal sphere $$=$$ volume of wire 
$$36\pi =\pi \times { 1 }^{ 2 }\times h\\ h=36 cm$$

Mathematics

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