Kilometers 31211

The road roller has a base diameter of 1.2 m and a length of 180 cm.
a) how many times did he turn on the road when he walked 2 km during work?
b) what is the largest area it can cover if it turns 1000 times?
c) how many kilometers will he travel if he covers 1050 m of road 3 times?

Correct answer:

n =  531
b =  6785.8401 m²
c =  3.15 km

Step-by-step explanation:

$$\begin{gathered} D=1.2\text{m} \\ l=180\text{cm}\to \text{m}=180:100\text{m}=1.8\text{m} \\ s=2\text{km}\to \text{m}=2\cdot 1000\text{m}=2000\text{m} \\ o=\pi \cdot D=3.1416\cdot 1.2\doteq 3.7699\text{m} \\ n=s/o=2000/3.7699=531 \end{gathered}$$

$$\begin{gathered} n_2=1000 \\ {S}_1=o\cdot l=3.7699\cdot 1.8\doteq 6.7858{\text{m}}^2 \\ b=n_2\cdot S_1=1000\cdot 6.7858=6785.8401{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} s_3=1050\text{m}\to \text{km}=1050:1000\text{km}=1.05\text{km} \\ c=3\cdot s_3=3\cdot 1.05=3.15\text{km} \end{gathered}$$

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