Traffic cones

Forty identical traffic cones with a base diameter d = 3 dm and a height v = 6 dm should be painted on the outside with orange paint (without base). How many crowns do we pay for color? If we need 50 cm³ of paint to paint, 1m² and 1l of paint costs CZK 80?

Correct answer:

x =  46.6312 Kc

Step-by-step explanation:

$$\begin{gathered} d=3\text{dm} \\ r=d/2=3/2=\frac{3}{2}=1.5\text{dm} \\ v=6\text{dm} \\ s=\sqrt{v^2+r^2}=\sqrt{6^2+1.5^2}\doteq 6.1847\text{dm} \\ {S}_1=\pi \cdot r\cdot s=3.1416\cdot 1.5\cdot 6.1847\doteq 29.1445{\text{dm}}^2 \\ {S}_2=1{\text{m}}^2\to {\text{dm}}^2=1\cdot 100{\text{dm}}^2=100{\text{dm}}^2 \\ n=40 \\ 1l=1d{m}^3 \\ c=80{\text{kc/dm}}^3 \\ {V}_1=50{\text{cm}}^3\to {\text{dm}}^3=50:1000{\text{dm}}^3=0.05{\text{dm}}^3 \\ k=c\cdot V_1/S_2=80\cdot 0.05/100=\frac{1}{25}=0.04{\text{Kc/dm}}^2 \\ x=n\cdot S_1\cdot k=40\cdot 29.1445\cdot 0.04=46.6312\text{Kc} \end{gathered}$$

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