Dimensions 82604

1 kg of cubed sugar consists of 840 cubes with an edge of 1.1 cm. Determine the sugar's density and the box's dimensions if the cubes are lined up in seven rows of nine cubes each. How many square meters of cardboard are needed to make 3000 boxes?

Correct answer:

ρ =  0.8944 g/cm³
a =  7.7 cm
b =  9.9 cm
c =  15.4 cm
S₁ =  694.54 cm²
S =  208.362 m²

Step-by-step explanation:

$$\begin{gathered} m=1\text{kg}\to \text{g}=1\cdot 1000\text{g}=1000\text{g} \\ n=840 \\ x=1.1\text{cm} \\ V=n\cdot x^3=840\cdot 1.1^3=\frac{27951}{25}=1118.04{\text{cm}}^3 \\ \rho =m/V=1000/1118.04=0.8944{\text{g/cm}}^3 \end{gathered}$$

$a=7\cdot x=7\cdot 1.1=7.7\text{cm}$

$b=9\cdot x=9\cdot 1.1=9.9\text{cm}$

$$\begin{gathered} k=ceil(n/(7\cdot 9))=ceil(840/(7\cdot 9))=14 \\ c=k\cdot x=14\cdot 1.1=15.4\text{cm} \end{gathered}$$

$S_1=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (7.7\cdot 9.9+9.9\cdot 15.4+15.4\cdot 7.7)=694.54{\text{cm}}^2$

$$\begin{gathered} m=3000 \\ {S}_2=S_1\to {\text{m}}^2=S_1:10000{\text{m}}^2=694.54:10000{\text{m}}^2=0.06945{\text{m}}^2 \\ S=m\cdot S_2=3000\cdot 0.0695=208.362{\text{m}}^2 \end{gathered}$$

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