Percentage + sphere

A sphere G is inscribed in the cube K with the length a. A cube K1 is inscribed in sphere G. What percentage of the volume of cube K is made up of the volume of cube K1?

Correct answer:

p =  19.245 %

Step-by-step explanation:

$$\begin{gathered} a=1 \\ r=a/2=1/2=\frac{1}{2}=0.5 \\ 2r=\sqrt{3}\cdot b \\ b=2\cdot r/\sqrt{3}=2\cdot 0.5/\sqrt{3}\doteq 0.5774 \\ {V}_1=a^3=1^3=1 \\ {V}_2=b^3=0.5774^3\doteq 0.1925 \\ p=100\cdot \frac{V_2}{V_1}=100\cdot \frac{0.1925}{1}=19.245\% \end{gathered}$$

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