Lump sugar

Cubed sugar in a 1 kg package is in a box with 20 cm, 12 cm, and 5 cm dimensions.

a) How many sugar cubes with dimensions 2.5 cm, 2.5 cm, and 1 cm fit in the box?
b) Calculate the mass of one cube.
c) How many square meters of cardboard are needed to make 1,000 boxes?

Final Answer:

n =  192
b =  5.2083 g
c =  80 m²

Step-by-step explanation:

$$\begin{gathered} x=20\text{cm} \\ y=12\text{cm} \\ z=5\text{cm} \\ {V}_1=x\cdot y\cdot z=20\cdot 12\cdot 5=1200{\text{cm}}^3 \\ {V}_2=2.5\cdot 2.5\cdot 1=6.25{\text{cm}}^3 \\ n=V_1/V_2=1200/6.25=192 \end{gathered}$$

$$\begin{gathered} m_0=1\text{kg}\to \text{g}=1\cdot 1000\text{g}=1000\text{g} \\ b=\frac{m_0}{n}=\frac{1000}{192}=5.2083\text{g} \end{gathered}$$

$$\begin{gathered} S_1=2\cdot (x\cdot y+y\cdot z+x\cdot z)=2\cdot (20\cdot 12+12\cdot 5+20\cdot 5)=800{\text{cm}}^2 \\ {S}_2=S_1\to {\text{m}}^2=S_1:10000{\text{m}}^2=800:10000{\text{m}}^2=0.08{\text{m}}^2 \\ c=1000\cdot S_2=1000\cdot 0.08=80{\text{m}}^2 \end{gathered}$$

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