Sand loading

The truck, with a load capacity of 7 tons, has a storage area of 4.5 m and 2.1 m. The weight of 1 m³ of wet sand is 2,000 kg. How high can we load the sand, so the car's load capacity is not exceeded?

Correct answer:

c =  0.3704 m

Step-by-step explanation:

$$\begin{gathered} m=7\text{t}\to \text{kg}=7\cdot 1000\text{kg}=7000\text{kg} \\ a=4.5\text{m} \\ b=2.1\text{m} \\ \rho =2000{\text{kg/m}}^3 \\ \rho =m/V \\ V=m/\rho =7000/2000=\frac{7}{2}=3.5{\text{m}}^3 \\ V=a\cdot b\cdot c \\ c=\frac{V}{a\cdot b}=\frac{3.5}{4.5\cdot 2.1}=\frac{10}{27}\text{m}=0.3704\text{m} \end{gathered}$$

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