Cone from cube

The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m3

Result

m =  1.78 kg

Solution:

a=20 cm ρ=850 kg/m3  r=a/2=20/2=10 cm h=a=20 cm V=13 π r2 h=13 3.1416 102 202094.3951 cm3  V1=Vm3=V/1000000 m3=2094.39510239/1000000 m3=0.00209 m3  m=ρ V1=850 0.00211.78021.78 kga=20 \ \text{cm} \ \\ ρ=850 \ \text{kg/m}^3 \ \\ \ \\ r=a/2=20/2=10 \ \text{cm} \ \\ h=a=20 \ \text{cm} \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r^2 \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 10^2 \cdot \ 20 \doteq 2094.3951 \ \text{cm}^3 \ \\ \ \\ V_{1}=V \rightarrow m^3=V / 1000000 \ m^3=2094.39510239 / 1000000 \ m^3=0.00209 \ m^3 \ \\ \ \\ m=ρ \cdot \ V_{1}=850 \cdot \ 0.0021 \doteq 1.7802 \doteq 1.78 \ \text{kg}



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