Truck load capacity

The load capacity of the truck is 10t. Will it carry 200 oak planks measuring 30 cm, 4 m, and 30 mm at a time if the weight of 1 dm³ of oak wood is 0.7 kg?

Final Answer:

m =  5.04 t

Step-by-step explanation:

$$\begin{gathered} n=200 \\ a=30\text{cm}\to \text{dm}=30:10\text{dm}=3\text{dm} \\ b=4\text{m}\to \text{dm}=4\cdot 10\text{dm}=40\text{dm} \\ c=30\text{mm}\to \text{dm}=30:100\text{dm}=0.3\text{dm} \\ \rho =0.7{\text{kg/dm}}^3 \\ V=a\cdot b\cdot c=3\cdot 40\cdot 0.3=36{\text{dm}}^3 \\ {m}_1=\rho \cdot V=0.7\cdot 36=\frac{126}{5}=25.2\text{kg} \\ {m}_2=n\cdot m_1=200\cdot 25.2=5040\text{kg} \\ m=m^2\to \text{t}=m^2:1000\text{t}=5040:1000\text{t}=5.04\text{t} \\ m<10t \end{gathered}$$

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