Cabinet painting

The cabinet is shaped like a block, with dimensions 120cm and 150cm on the front side and 120cm and 60cm on the upper wall. It is painted twice on the outside. When 1 kg of paint is enough to paint 8m², how much paint is used to paint the cabinet?

Final Answer:

m =  1.71 kg

Step-by-step explanation:

$$\begin{gathered} a=120\text{cm}\to \text{m}=120:100\text{m}=1.2\text{m} \\ b=150\text{cm}\to \text{m}=150:100\text{m}=1.5\text{m} \\ c=60\text{cm}\to \text{m}=60:100\text{m}=0.6\text{m} \\ \sigma =1/8=\frac{1}{8}=0.125{\text{kg/m}}^2 \\ S=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (1.2\cdot 1.5+1.5\cdot 0.6+0.6\cdot 1.2)=\frac{171}{25}=6.84{\text{m}}^2 \\ m=2\cdot \sigma \cdot S=2\cdot 0.125\cdot 6.84=1.71\text{kg} \end{gathered}$$

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