Cube containers

Two containers shaped as cubes with edges of 0.7 m and 0.9 m replace a single cube so that it has the same volume as the original two together. What is the length of the edges of the new cube?

Correct answer:

a =  1.0234 m

Step-by-step explanation:

$$\begin{gathered} x=0.7\text{m} \\ y=0.9\text{m} \\ {V}_1=x^3=0.7^3=\frac{343}{1000}=0.343{\text{m}}^3 \\ {V}_2=y^3=0.9^3=\frac{729}{1000}=0.729{\text{m}}^3 \\ V=a^3=V_1+V_2 \\ {a}^3=V_1+V_2 \\ a=\sqrt[3]{V_1+V_2}=\sqrt[3]{0.343+0.729}=1.0234\text{m} \end{gathered}$$

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