Costume

Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand Denise's hair has a length of 0.5 m a diameter 60 μm and a cylinder shape. The density of gold is 19,000 kg·m-3.

Correct result:

m =  969.9667 g

Solution:

$$\begin{gathered} h=19 \\ {r}_2=60\mathrm{/}1000\mathrm{/}10\mathrm{/}2={\displaystyle \frac{3}{1000}}=0.003 \\ {r}_1=r_2+5\mathrm{/}1000\mathrm{/}10=0.003+5\mathrm{/}1000\mathrm{/}10={\displaystyle \frac{7}{2000}}=0.0035 \\ V=50\cdot (\pi \cdot r_1^2-\pi \cdot r_2^2)=50\cdot (3.1416\cdot 0.0035^2-3.1416\cdot 0.003^2)\doteq 0.0005 \\ {m}_1=h\cdot V=19\cdot 0.0005\doteq 0.0097 \\ m=100000\cdot m_1=100000\cdot 0.0097=969.9667\text{ g} \end{gathered}$$

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