Percentage 39373

A sphere is placed inside the 10 cm cube to touch all the cube's walls. What percentage of the volume of a cube makes up the volume of a sphere?

Correct answer:

p =  52.3599 %

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ r=a/2=10/2=5\text{cm} \\ {V}_1=4/3\pi \cdot r^3=4/3\cdot 3.1416\cdot 5^3\doteq 523.5988{\text{cm}}^3 \\ {V}_2=a^3=10^3=1000{\text{cm}}^3 \\ p=100\cdot V_1/V_2=100\cdot 523.5988/1000=52.3599\% \end{gathered}$$

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