Cylinder Paint Weight Area

The sheet metal keg for oil transport has the shape of a cylinder with a volume of 62.8 liters and a height of 0.5 m. How many kg of paint do we need to paint if we need 1 kg of paint for 1.5 m²?

Final Answer:

m =  0.5862 kg

Step-by-step explanation:

$$\begin{gathered} V=62.8\text{l}\to {\text{m}}^3=62.8:1000{\text{m}}^3=0.0628{\text{m}}^3 \\ h=0.5\text{m} \\ {S}_1=V/h=0.0628/0.5=\frac{157}{1250}=0.1256{\text{m}}^2 \\ f=1/1.5=\frac{2}{3}\doteq 0.6667{\text{kg/m}}^2 \\ {S}_1=\pi r^2 \\ r=\sqrt{S_1/\pi }=\sqrt{0.1256/3.1416}\doteq 0.1999\text{m} \\ S=2\cdot S_1+2\pi \cdot r\cdot h=2\cdot 0.1256+2\cdot 3.1416\cdot 0.1999\cdot 0.5\doteq 0.8794{\text{m}}^2 \\ m=S\cdot f=0.8794\cdot 0.6667=0.5862\text{kg} \end{gathered}$$

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