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 of 60 μm, and a cylinder shape. The density of gold is 19,000 kg·m-3.

Correct answer:

m =  969.9667 g

Step-by-step explanation:

$$\begin{gathered} h=19{\text{g/cm}}^3 \\ {D}_2=60/1000/10=\frac{3}{500}=0.006\text{cm} \\ {r}_2=D_2/2=0.006/2=\frac{3}{1000}=0.003\text{cm} \\ {r}_1=r_2+5/1000/10=0.003+5/1000/10=\frac{7}{2000}=0.0035\text{cm} \\ V=50\cdot (\pi \cdot r_1^2-\pi \cdot r_2^2)=50\cdot (3.1416\cdot 0.0035^2-3.1416\cdot 0.003^2)\doteq 0.0005{\text{cm}}^3 \\ {m}_1=h\cdot V=19\cdot 0.0005\doteq 0.0097\text{g} \\ m=100000\cdot m_1=100000\cdot 0.0097=969.9667\text{g} \end{gathered}$$

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