Truck bed

Calculate how many truckloads are needed to transport grain from the combine hopper. The hopper is a prism with a rhombus-shaped base with sides of 13 dm and a height of 2.8 m to the longest side. The hopper is 200 cm long. The truck bed is a cuboid with dimensions of 5 m × 3.5 m × 50 cm.

Final Answer:

n =  0.5943

Step-by-step explanation:

$$\begin{gathered} a=13\text{dm}\to \text{m}=13:10\text{m}=1.3\text{m} \\ b=2.8\text{m} \\ v=200\text{cm}\to \text{m}=200:100\text{m}=2\text{m} \\ h=200\text{cm}\to \text{m}=200:100\text{m}=2\text{m} \\ x=5\text{m} \\ y=3.5\text{m} \\ z=50\text{cm}\to \text{m}=50:100\text{m}=0.5\text{m} \\ {V}_1=a\cdot v\cdot h=1.3\cdot 2\cdot 2=\frac{26}{5}=5\frac{1}{5}=5.2{\text{m}}^3 \\ {V}_2=x\cdot y\cdot z=5\cdot 3.5\cdot 0.5=\frac{35}{4}=8\frac{3}{4}=8.75{\text{m}}^3 \\ n=V_1/V_2=5.2/8.75=0.5943 \end{gathered}$$

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