Inscribed sphere

How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?

Correct answer:

p =  52.3599 %

Step-by-step explanation:

$$\begin{gathered} a=6\text{ m } \\ r=a\mathrm{/}2=6\mathrm{/}2=3\text{ m } \\ {V}_1=4\mathrm{/}3\pi \cdot r^3=4\mathrm{/}3\cdot 3.1416\cdot 3^3\doteq 113.0973{\text{m}}^3 \\ {V}_2=a^3=6^3=216{\text{m}}^3 \\ p=100\cdot V_1\mathrm{/}{V}_2=100\cdot 113.0973\mathrm{/}216=52.3599\mathrm{\%} \end{gathered}$$

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