Six-tonne truck

The platform of a six-tonne truck is 2.20 m wide and 4.20 m long; the side panels are 0.75 m high.

How many cubic metres of gravel could be loaded onto the truck with a well-levelled load up to the height of the side panels?

How deep a layer of gravel can be loaded without exceeding the vehicle's load capacity of 6 tonnes, given that 1 cubic metre of gravel has a mass of 1.8 t?

Final Answer:

V =  6.93 m³
x =  0.3608 m

Step-by-step explanation:

$$\begin{gathered} a=2.20\text{m} \\ b=4.20\text{m} \\ c=0.75\text{m} \\ V=a\cdot b\cdot c=2.2\cdot 4.2\cdot 0.75=6.93{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} m_1=6\text{t} \\ \rho =1.8{\text{t/m}}^3 \\ {V}_1=m_1/\rho =6/1.8=\frac{10}{3}\doteq 3.3333{\text{m}}^3 \\ {V}_1=a\cdot b\cdot x \\ x=\frac{V_1}{a\cdot b}=\frac{3.3333}{2.2\cdot 4.2}=0.3608\text{m} \end{gathered}$$

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