Pool excavation transport

The Mokry family wants to build a pool in the garden, which has the shape of a cuboid with dimensions of 3 m wide, 5 m long, and 1.20 m deep. They need to dig a hole whose dimensions will be 70 cm larger than the dimensions of the pool. How often does the truck turn when importing the excavated earth to the landfill? Ok, its anchor volume is 7 m³.

Final Answer:

n =  8

Step-by-step explanation:

$$\begin{gathered} a=3\text{m} \\ b=5\text{m} \\ c=1.2\text{m} \\ x=70\text{cm}\to \text{m}=70:100\text{m}=0.7\text{m} \\ {V}_1=7{\text{m}}^3 \\ V=(a+2\cdot x)\cdot (b+2\cdot x)\cdot (c+x)=(3+2\cdot 0.7)\cdot (5+2\cdot 0.7)\cdot (1.2+0.7)=\frac{6688}{125}=53\frac{63}{125}=53.504{\text{m}}^3 \\ n=\lceil V/V_1\rceil =\lceil 53.504/7\rceil =8 \end{gathered}$$

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