Quadrilateral prism

The diagonal of section DBFH of the regular quadrilateral prism ABCDEFGH inscribes a circle with a diameter of 8 cm. What is the volume of the prism?

Final Answer:

V =  64 cm³

Step-by-step explanation:

$$\begin{gathered} d=8\text{cm} \\ r=d/2=8/2=4\text{cm} \\ c=|BF| \\ u=|BD| \\ c=d=8\text{cm} \\ u=d=8\text{cm} \\ u=\sqrt{2}\cdot a \\ a=u/\sqrt{u}=8/\sqrt{8}=2\sqrt{2}\text{cm}\doteq 2.8284\text{cm} \\ V=a^2\cdot c=2.8284^2\cdot 8=64{\text{cm}}^3 \end{gathered}$$

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