3d printer

3D printing ABS filament with a diameter of 1.75 mm has a density of 1.04 g/cm³. Find the length of m = 5 kg spool filament. (how to calculate length)

Correct answer:

l =  1998.8062 m

Step-by-step explanation:

$$\begin{gathered} D=1.75\text{mm}\to \text{cm}=1.75:10\text{cm}=0.175\text{cm} \\ d=1.04{\text{g/cm}}^3 \\ m=5\text{kg}\to \text{g}=5\cdot 1000\text{g}=5000\text{g} \\ r=D/2=0.175/2=\frac{7}{80}=0.0875\text{cm} \\ S=\pi \cdot r^2=3.1416\cdot 0.0875^2\doteq 0.0241{\text{cm}}^2 \\ V=m/d=5000/1.04=\frac{62500}{13}\doteq 4807.6923{\text{cm}}^3 \\ {l}_1=V/S=4807.6923/0.0241\doteq 199880.6193 \\ l=l_1\to \text{m}=l_1:100\text{m}=199880.6193:100\text{m}=1998.806\text{m}=1998.8062\text{m} \end{gathered}$$

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