Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent was the waste.

Correct answer:

p =  47.6401 %

Step-by-step explanation:

$$\begin{gathered} a=1 \\ r=a\mathrm{/}2=1\mathrm{/}2={\displaystyle \frac{1}{2}}=0.5 \\ {V}_1=a^3=1^3=1 \\ {V}_2={\displaystyle \frac{4}{3}}\cdot \pi \cdot r^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 0.5^3\doteq 0.5236 \\ p=100\cdot {\displaystyle \frac{V_1-V_2}{V_1}}=100\cdot {\displaystyle \frac{1-0.5236}{1}}=47.6401\mathrm{\%} \end{gathered}$$

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