Cylinder in cube

A can in the shape of a cylinder with a height of 10 cm and touching all the walls of the cube is placed into a paper box in the shape of a cube with an edge of 10 cm. What % of the cube's volume can it take up?

Correct answer:

p =  78.5398 %

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ r=a/2=10/2=5\text{cm} \\ {S}_1=a^2=10^2=100{\text{cm}}^2 \\ {S}_2=\pi \cdot r^2=3.1416\cdot 5^2\doteq 78.5398{\text{cm}}^2 \\ p=100\cdot \frac{V_2}{V_1}=100\cdot \frac{a\cdot S_2}{a\cdot S_1} \\ p=100\cdot \frac{S_2}{S_1}=100\cdot \frac{78.5398}{100}=78.5398\% \end{gathered}$$

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