Two rectangular boxes

Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.

Correct result:

S =  600 cm²

Solution:

$$\begin{gathered} V_1=5\cdot 8\cdot 10=400{\text{cm}}^3 \\ {V}_2=5\cdot 12\cdot 10=600{\text{cm}}^3 \\ V=V_1+V_2=400+600=1000{\text{cm}}^3 \\ V=a^3 \\ a=\sqrt[3]{V}=\sqrt[3]{1000}=10\text{ cm } \\ S=6\cdot a^2=6\cdot 10^2=600{\text{cm}}^2 \end{gathered}$$

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