3d printer

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

Result

l =  1998.806 m

Solution:

$D=1.75 \ mm=1.75 / 10 \ cm=0.175 \ cm \ \\ d=1.04 \ \text{g/cm}^3 \ \\ m=5 \ kg=5 \cdot \ 1000 \ g=5000 \ g \ \\ \ \\ r=D/2=0.175/2=\dfrac{ 7 }{ 80 }=0.0875 \ \text{cm} \ \\ S=\pi \cdot \ r ^2=3.1416 \cdot \ 0.0875 ^2 \doteq 0.0241 \ \text{cm}^2 \ \\ \ \\ V=m/d=5000/1.04 \doteq \dfrac{ 62500 }{ 13 } \doteq 4807.6923 \ \text{cm}^3 \ \\ \ \\ l_{1}=V/S=4807.6923/0.0241 \doteq 199880.6193 \ \\ l=l_{1} \rightarrow m=l_{1} / 100 \ m=1998.80619 \ m=1998.806 \ \text{m}$

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