Cube containers

Replace the two cube-shaped containers with 0.8 dm and 0.6 dm edges with a single cube-shaped one so that it has the same volume as the two original ones together. What is the length of the edge of this cube?

Correct answer:

c =  0.8996 dm

Step-by-step explanation:

$$\begin{gathered} a=0.8\text{dm} \\ b=0.6\text{dm} \\ {V}_1=a^3=0.8^3=\frac{64}{125}=0.512{\text{dm}}^3 \\ {V}_2=b^3=0.6^3=\frac{27}{125}=0.216{\text{dm}}^3 \\ V=V_1+V_2=0.512+0.216=\frac{91}{125}=0.728{\text{dm}}^3 \\ V=c^3 \\ c=\sqrt[3]{V}=\sqrt[3]{0.728}=0.8996\text{dm} \end{gathered}$$

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