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.

Result

S =  600 cm2

Solution:

V1=5 8 10=400 cm3 V2=5 12 10=600 cm3  V=V1+V2=400+600=1000 cm3  V=a3  a=V3=10003=10 cm  S=6 a2=6 102=600 cm2V_{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



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