Percentage 61594

Calculate the percentage of the cube volume that represents the volume of the cylinder inscribed in the cube. The cylinder's bases are circles inscribed on two opposite walls of the cube with an edge a = 14 cm.

Correct answer:

p =  78.5398 %

Step-by-step explanation:

$$\begin{gathered} a=14\text{cm} \\ r=a/2=14/2=7\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 7^2\doteq 153.938{\text{cm}}^2 \\ {S}_2=a^2=14^2=196{\text{cm}}^2 \\ {V}_1=S_1\cdot a \\ {V}_2=S_2\cdot a \\ p=100\cdot \frac{V_1}{V_2} \\ p=100\cdot \frac{S_1}{S_2}=100\cdot \frac{153.938}{196}=78.5398\% \end{gathered}$$

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