Carefully 12791

Spruce logs with a diameter of 270 mm and a length of 4 m are carefully loaded onto a wagon with a bed width of 2,700 mm and stacked in 9 layers. How much does such a load of spruce wood weigh if its density is 700 kg/m³?

Correct answer:

m =  14.4284 t

Step-by-step explanation:

$$\begin{gathered} l=2700\text{mm}\to \text{m}=2700:1000\text{m}=2.7\text{m} \\ n=9 \\ D=270\text{mm}\to \text{m}=270:1000\text{m}=0.27\text{m} \\ {l}_1=4\text{m} \\ \rho =700{\text{kg/m}}^3 \\ r=D/2=0.27/2=\frac{27}{200}=0.135\text{m} \\ {V}_1=\pi \cdot r^2\cdot l_1=3.1416\cdot 0.135^2\cdot 4\doteq 0.229{\text{m}}^3 \\ {m}_1=\rho \cdot V_1=700\cdot 0.229\doteq 160.3155\text{kg} \\ {n}_2=n\cdot (l/D)=9\cdot (2.7/0.27)=90 \\ {m}_2=n_2\cdot m_1=90\cdot 160.3155\doteq 14428.3926\text{kg} \\ m=m^2\to \text{t}=m^2:1000\text{t}=14428.3926:1000\text{t}=14.428\text{t}=14.4284\text{t} \end{gathered}$$

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