Barrel painting calculation

The water barrel, 90 cm high and 60 cm wide, has no lid (upper base). How much paint do we need to paint the barrel from the outside? If 1 kg of paint is enough for 8m².

Final Answer:

x =  0.2474 kg

Step-by-step explanation:

$$\begin{gathered} h=90\text{cm}\to \text{m}=90:100\text{m}=0.9\text{m} \\ D=60\text{cm}\to \text{m}=60:100\text{m}=0.6\text{m} \\ r=D/2=0.6/2=\frac{3}{10}=0.3\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 0.3^2\doteq 0.2827{\text{m}}^2 \\ {S}_2=\pi \cdot D\cdot h=3.1416\cdot 0.6\cdot 0.9\doteq 1.6965{\text{m}}^2 \\ S=S_1+S_2=0.2827+1.6965\doteq 1.9792{\text{m}}^2 \\ \rho =1/8=\frac{1}{8}=0.125{\text{kg/m}}^2 \\ x=\rho \cdot S=0.125\cdot 1.9792=0.2474\text{kg} \end{gathered}$$

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