Dimensions - cardboard

The statements are sold in cardboard boxes – for example, the microwave oven box has dimensions of 52 cm, 32 cm, and 40 cm, and 0.4 m² of cardboard is added to the folds. How many square meters of cardboard are needed for 1,000 boxes?

Final Answer:

S =  1404.8 m²

Step-by-step explanation:

$$\begin{gathered} a=52\text{cm}\to \text{m}=52:100\text{m}=0.52\text{m} \\ b=32\text{cm}\to \text{m}=32:100\text{m}=0.32\text{m} \\ c=40\text{cm}\to \text{m}=40:100\text{m}=0.4\text{m} \\ {S}_1=0.4{\text{m}}^2 \\ {S}_2=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (0.52\cdot 0.32+0.32\cdot 0.4+0.4\cdot 0.52)=\frac{628}{625}=1.0048{\text{m}}^2 \\ n=1000 \\ S=1000\cdot (S_1+S_2)=1000\cdot (0.4+1.0048)=1404.8{\text{m}}^2 \end{gathered}$$

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