Concrete pipe

How much will it cost to cover a 6 m long concrete pipe with an outer radius of 1.5 m and an inner radius of 0.8 meters if one m² paint costs 24 €?

Correct answer:

x =  1101.19 Eur

Step-by-step explanation:

$$\begin{gathered} a=6\text{m} \\ D=1.5\text{m} \\ d=0.8\text{m} \\ c=24{\text{Eur/m}}^2 \\ {r}_1=D/2=1.5/2=\frac{3}{4}=0.75\text{m} \\ {r}_2=d/2=0.8/2=\frac{2}{5}=0.4\text{m} \\ {S}_1=a\cdot \pi \cdot D=6\cdot 3.1416\cdot 1.5\doteq 28.2743{\text{m}}^2 \\ {S}_2=a\cdot \pi \cdot d=6\cdot 3.1416\cdot 0.8\doteq 15.0796{\text{m}}^2 \\ {S}_3=\pi \cdot r_1^2-\pi \cdot r_2^2=3.1416\cdot 0.75^2-3.1416\cdot 0.4^2\doteq 1.2645{\text{m}}^2 \\ S=S_1+S_2+2\cdot S_3=28.2743+15.0796+2\cdot 1.2645\doteq 45.883{\text{m}}^2 \\ x=c\cdot S=24\cdot 45.883=1101.19\text{Eur} \end{gathered}$$

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