Body diagonal

The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?

Correct result:

u =  6 cm

Solution:

V=a2 c=32 4 a c=2 a2 2c=a 4c2 c=32 c3=8 c=83=2 a=2 c=2 2=4 u=a2+a2+c2=42+42+22=6 cmV=a^2 \ c=32 \ \\ 4 \cdot \ a \cdot \ c=2 \ a^2 \ \\ 2c=a \ \\ 4c^2 \ c=32 \ \\ c^3=8 \ \\ c=\sqrt[3]{ 8 }=2 \ \\ a=2 \cdot \ c=2 \cdot \ 2=4 \ \\ u=\sqrt{ a^2+a^2+c^2 }=\sqrt{ 4^2+4^2+2^2 }=6 \ \text{cm}



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