Cube cylinder volume

There is a cylinder with the largest possible volume in the cube with an edge of 6 m. What percentage of the volume of a cube has the volume of a cylinder?

Final Answer:

p =  78.5398 %

Step-by-step explanation:

$$\begin{gathered} a=6\text{m} \\ r=a/2=6/2=3\text{m} \\ {V}_1=a^3=6^3=216{\text{m}}^3 \\ {V}_2=\pi \cdot r^2\cdot a=3.1416\cdot 3^2\cdot 6\doteq 169.646{\text{m}}^3 \\ p=100\cdot \frac{V_2}{V_1}=100\cdot \frac{169.646}{216}=78.5398\% \end{gathered}$$

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