Well excavation transport

The company is to dig a well 25 m deep with a radius of 0.8 m. How many cars that can be loaded with 12 cubic m will be needed to transport the excavated soil if it is calculated that the soil will increase in volume by 10% when excavated?

Final Answer:

n =  5

Step-by-step explanation:

$$\begin{gathered} h=25\text{m} \\ r=0.8\text{m} \\ {V}_1=12{\text{m}}^3 \\ q=100\%+10\%=1+\frac{10}{100}=1.1 \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 0.8^2\cdot 25\doteq 50.2655{\text{m}}^3 \\ {V}_2=V\cdot q=50.2655\cdot 1.1\doteq 55.292{\text{m}}^3 \\ {n}_1=V_2/V_1=55.292/12\doteq 4.6077 \\ n=\lceil n_1\rceil =\lceil 4.6077\rceil =5 \end{gathered}$$

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