# Flower boxes

How many m2 of 10mm thick boards are needed to make 12 flower boxes? The dimensions of the box are 180,150 and 1500 mm.

Correct result:

x =  11.659 m2

#### Solution:

$h=10 \ \text{mm} \ \\ n=12 \ \\ a=180 \ \text{mm} \ \\ b=150 \ \text{mm} \ \\ c=1500 \ \text{mm} \ \\ \ \\ V_{1}=a \cdot \ b \cdot \ c=180 \cdot \ 150 \cdot \ 1500=40500000 \ \text{mm}^3 \ \\ V_{2}=(a-2 \cdot \ h) \cdot \ (b-2 \cdot \ h) \cdot \ (c-2 \cdot \ h)=(180-2 \cdot \ 10) \cdot \ (150-2 \cdot \ 10) \cdot \ (1500-2 \cdot \ 10)=30784000 \ \text{mm}^3 \ \\ \ \\ V_{3}=V_{1}-V_{2}=40500000-30784000=9716000 \ \text{mm}^3 \ \\ \ \\ S_{1}=V_{3}/h=9716000/10=971600 \ \text{mm}^2 \ \\ \ \\ S_{2}=S_{1} \rightarrow dm^2=S_{1} / 10000 \ dm^2=971600 / 10000 \ dm^2=97.16 \ dm^2 \ \\ S_{3}=S_{2} \rightarrow m^2=S_{2} / 100 \ m^2=97.16 / 100 \ m^2=0.9716 \ m^2 \ \\ \ \\ x=n \cdot \ S_{3}=12 \cdot \ 0.9716=\dfrac{ 7287 }{ 625 }=11.659 \ \text{m}^2$

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