Sugar bowl cubes

A) Can the maximum number of sugar cubes with a volume of 3375 cubic mm fit in a new cube-shaped sugar bowl with internal dimensions of 12 cm, 6 cm, and 3 cm?

B) Mom poured sugar cubes into the new sugar bowl, filling it completely. She estimated that there was about 15% free space left in it. About how many sugar cubes are in a sugar bowl?

Final Answer:

n =  64
n₂ =  54

Step-by-step explanation:

$$\begin{gathered} V_1=3375{\text{mm}}^3\to {\text{cm}}^3=3375:1000{\text{cm}}^3=3.375{\text{cm}}^3 \\ a=12\text{cm} \\ b=6\text{cm} \\ c=3\text{cm} \\ V=a\cdot b\cdot c=12\cdot 6\cdot 3=216{\text{cm}}^3 \\ {V}_1=x^3 \\ x=\sqrt[ \\ 3]{V_1}=\sqrt[ \\ 3]{3.375}=\frac{3}{2}=1\frac{1}{2}=1.5\text{cm} \\ n=V/V_1=216/3.375=64 \end{gathered}$$

$$\begin{gathered} q=100\%-15\%=1-\frac{15}{100}=0.85 \\ {V}_2=q\cdot V=0.85\cdot 216=\frac{918}{5}=183\frac{3}{5}=183.6{\text{cm}}^3 \\ {n}_2=\lfloor V_2/V_1\rfloor =\lfloor 183.6/3.375\rfloor =54 \end{gathered}$$

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