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A cubic cm of gold is drawn into a wire 0.1mm in diameter, find the length of the wire

Posted by Roushan & Suraj 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given,
Volume of gold = 1 cm³= 1000 mm³ ......(1)
Diameter of wire = 0.1 mm
Radius of wire = {tex}\frac { 0.1 } { 2 }{/tex} = 0.05 mm
Let, the length of the wire = h mm
According to the question,
Volume of wire = Volume of gold
{tex}\Rightarrow {/tex} πr²h = 1000 .( Since, wire is cylindrical & from (1) )
{tex}\Rightarrow π× ( 0.05 ) ^ { 2 } \times h{/tex} = 1000
{tex}\Rightarrow \frac { 22 } { 7 } \times 0.0025 \times h{/tex} = 1000
{tex}\Rightarrow h = \frac { 1000 \times 7 } { 22 \times 0.0025 }{/tex}mm
{tex}\Rightarrow{/tex} h = 127272.72 mm
{tex}\Rightarrow{/tex} h = 127.27 m(approx.)

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