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 answer:

u =  6 cm

Step-by-step explanation:

$$\begin{gathered} V=32{\text{cm}}^2 \\ V=a^{2}c \\ {S}_1=2\cdot S_2 \\ (4\cdot a\cdot c)=2\cdot a^2 \\ 2\cdot a\cdot c=a^2 \\ 2c=a \\ 2c=a \\ 4c^{2}c=32 \\ {c}^3=8 \\ c=\sqrt[3]{8}=2 \\ a=2\cdot c=2\cdot 2=4 \\ u=\sqrt{a^2+a^2+c^2}=\sqrt{4^2+4^2+2^2}=6=6\text{ cm } \\ \text{ Verifying Solution: } \\ c=a\mathrm{/}2=4\mathrm{/}2=2\text{ cm } \\ {V}_2=a^2\cdot c=4^2\cdot 2=32{\text{cm}}^3 \\ {S}_1=4\cdot a\cdot c=4\cdot 4\cdot 2=32{\text{cm}}^2 \\ {S}_2=a^2=4^2=16{\text{cm}}^2 \end{gathered}$$

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