Cone from cube

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

Correct answer:

m =  1.7802 kg

Step-by-step explanation:

$$\begin{gathered} a=20\text{cm} \\ \rho =850{\text{kg/m}}^3 \\ r=a/2=20/2=10\text{cm} \\ h=a=20\text{cm} \\ V=\frac{1}{3}\cdot \pi \cdot r^2\cdot h=\frac{1}{3}\cdot 3.1416\cdot 10^2\cdot 20\doteq 2094.3951{\text{cm}}^3 \\ {V}_1=V\to {\text{m}}^3=V:1000000{\text{m}}^3=2094.3951:1000000{\text{m}}^3=0.00209{\text{m}}^3 \\ m=\rho \cdot V_1=850\cdot 0.0021=1.7802\text{kg} \end{gathered}$$

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