Cubes into cuboid

How many 12 centimeter cubes fit into the block (cuboid) with 6dm, 8.4dm, and 4.8?

Correct answer:

n =  140

Step-by-step explanation:

$$\begin{gathered} a_1=12\mathrm{/}10={\displaystyle \frac{6}{5}}=1\frac{1}{5}=1.2\text{ dm } \\ {V}_1=a_1^3=1.2^3={\displaystyle \frac{216}{125}}=1\frac{91}{125}=1.728{\text{dm}}^3 \\ a=6\text{ dm } \\ b=8.4\text{ dm } \\ c=4.8\text{ dm } \\ {V}_2=a\cdot b\cdot c=6\cdot 8.4\cdot 4.8={\displaystyle \frac{6048}{25}}=241\frac{23}{25}=241.92{\text{dm}}^3 \\ n=V_2\mathrm{/}{V}_1=241.92\mathrm{/}1.728=140 \end{gathered}$$

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