Box paper calculation

How many m² of paper are needed to produce 1000 pieces of cube-shaped boxes with an 8 cm edge when we must add one-quarter of the area to the joints?

Final Answer:

S =  48 m²

Step-by-step explanation:

$$\begin{gathered} n=1000 \\ a=8\text{cm} \\ q=1+\frac{1}{4}=\frac{1\cdot 4}{4}+\frac{1}{4}=\frac{4}{4}+\frac{1}{4}=\frac{4+1}{4}=\frac{5}{4}=1.25 \\ {S}_1=6\cdot a^2=6\cdot 8^2=384{\text{cm}}^2 \\ {S}_2=S_1\cdot q\cdot n=384\cdot \frac{5}{4}\cdot 1000=480000{\text{cm}}^2 \\ S=S_2\to {\text{m}}^2=S_2:10000{\text{m}}^2=480000:10000{\text{m}}^2=48{\text{m}}^2=48{\text{m}}^2 \end{gathered}$$

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