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in Mensuration by (35.6k points)
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The diameter of a metallic sphere is 6 cm. It is melted and drawn into a wire having diameter as 2 cm. Then the length of the wire (in cm) …………

A) 48 

B) 12 

C) 36 

D) 24

2 Answers

+1 vote
by (66.4k points)
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Best answer

Correct option is: C) 36

Radius of metallic sphere is R = \(\frac {Diameter}{2}\) = \(\frac 62\) = 3 cm.

Radius of wire is r = \(\frac {Diameter}{2}\) = \(\frac 22\) = 1 cm.

\(\therefore\) Volume of wire = Volume of metallic sphere

\(\Rightarrow\) \(\pi r^2h\) = \(\frac 43 \pi r^3\) (\(\because\) Wire is in cylindrical shape)

\(\Rightarrow\) h = \(\frac {\frac 43 R^3}{r^2} = \frac 43 \times \frac {3 \times 3 \times 3}{1 \times1} = 36 \, cm\) 

Hence, the length of the wire is 36 cm.

+1 vote
by (34.5k points)

Correct option is: C) 36

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