Cylinder in cube

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

Correct result:

p =  78.5398 %

Solution:

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

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