Three cubes

Two cube-shaped boxes with edges a = 70 cm; b = 90 cm must be replaced by one cube-shaped box. What will be its edge?

Correct answer:

c =  102.3446 cm

Step-by-step explanation:

$$\begin{gathered} a=70\text{ cm } \\ b=90\text{ cm } \\ {V}_1=a^3=70^3=343000{\text{cm}}^3 \\ {V}_2=b^3=90^3=729000{\text{cm}}^3 \\ V=V_1+V_2=343000+729000=1072000{\text{cm}}^3 \\ V=c^3 \\ c=\sqrt[3]{V}=\sqrt[3]{1072000}=102.3446\text{ cm} \end{gathered}$$

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